تكلم مع الذكاء الاصطناعي
Deck 5: Integration
ملء الشاشة (f)
سؤال
Find the function 
satisfying the given conditions. 
A)
B)
C)
D)
satisfying the given conditions. A)
B)
C)
D)
سؤال
Suppose that a car can accelerate from 
mph to 
mph in 
seconds. Assuming a constant acceleration, find the acceleration (in miles per second squared) of the car and find the distance traveled by the car during the 
seconds.
A) Acceleration =
m/s22; distance = 
miles
B) Acceleration =
m/s22; distance = 
miles
C) Acceleration =
m/s22; distance = 
miles
D) Acceleration =
m/s22; distance = 
miles
mph to mph in seconds. Assuming a constant acceleration, find the acceleration (in miles per second squared) of the car and find the distance traveled by the car during the seconds.A) Acceleration =
m/s22; distance = milesB) Acceleration =
m/s22; distance = milesC) Acceleration =
m/s22; distance = milesD) Acceleration =
m/s22; distance = miles سؤال
Suppose that a car can come to rest from 
mph in 
seconds. Assuming a constant (negative) acceleration, find the acceleration (in miles per second squared) of the car and find the distance traveled by the car during the 
seconds (i.e., the stopping distance).
A) Acceleration =
m/s2; distance = 
miles
B) Acceleration =
m/s2; distance = 
miles
C) Acceleration =
m/s2; distance = 
miles
D) Acceleration =
m/s2; distance = 
miles
mph in seconds. Assuming a constant (negative) acceleration, find the acceleration (in miles per second squared) of the car and find the distance traveled by the car during the seconds (i.e., the stopping distance).A) Acceleration =
m/s2; distance = milesB) Acceleration =
m/s2; distance = milesC) Acceleration =
m/s2; distance = milesD) Acceleration =
m/s2; distance = miles سؤال
Find the general antiderivative. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Find the function 
satisfying the given conditions. 
A)
B)
C)
D)
satisfying the given conditions. A)
B)
C)
D)
سؤال
Find all functions satisfying the given conditions. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Find the general antiderivative. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Find an antiderivative by reversing the chain rule, product rule or quotient rule. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Find the general antiderivative. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Determine the position function if the velocity function is 
and the initial position is 
.
A)
B)
C)
D)
and the initial position is .A)
B)
C)
D)
سؤال
Find an antiderivative by reversing the chain rule, product rule or quotient rule. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Sketch a graph of a function 
corresponding to the given graph of 
. 
corresponding to the given graph of . سؤال
Determine the position function if the acceleration function is 
, the initial velocity is 
, and the initial position is 
.
A)
B)
C)
D)
, the initial velocity is , and the initial position is .A)
B)
C)
D)
سؤال
Find all functions satisfying the given conditions. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Sketch a graph of a function 
corresponding to the given graph of 
. 
corresponding to the given graph of . سؤال
The following table shows the velocity of a falling object at different times. For each time interval, estimate the distance fallen and the acceleration. Round to two decimal places. 
سؤال
Find an antiderivative by reversing the chain rule, product rule, or quotient rule. 
سؤال
Find the general antiderivative. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Find the general antiderivative. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Find the general antiderivative. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Translate into summation notation. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Use summation rules to compute the sum. 
A) 2264
B) 30,784
C) 39,964
D) 2804
A) 2264
B) 30,784
C) 39,964
D) 2804
سؤال
Use formulas to compute the sum. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Write out all terms and compute the sum. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Use summation rules to compute the sum. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Compute the sum and the limit of the sum as 
. 
A) Sum =
; limit of sum as 
is 
B) Sum =
; limit of sum as 
is 
C) Sum =
; limit of sum as 
is 
D) Sum =
; limit of sum as 
is 
. A) Sum =
; limit of sum as is B) Sum =
; limit of sum as is C) Sum =
; limit of sum as is D) Sum =
; limit of sum as is سؤال
Use mathematical induction to prove that 
for all integers 
.
for all integers . سؤال
List the evaluation points corresponding to the midpoint of each subinterval, and evaluate the corresponding Riemann sum. Round the sum to two decimal places. 
A) Evaluation points:
Riemann sum:
B) Evaluation points:
Riemann sum:
C) Evaluation points:
Riemann sum:
D) Evaluation points:
Riemann sum:
A) Evaluation points:
Riemann sum:
B) Evaluation points:
Riemann sum:
C) Evaluation points:
Riemann sum:
D) Evaluation points:
Riemann sum:
سؤال
Use summation rules to compute the sum. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
The following table shows the acceleration of a car moving in a straight line. If the car is traveling 
ft/s at time 
, estimate the speed and distance traveled at each time. 
ft/s at time , estimate the speed and distance traveled at each time. سؤال
Compute the sum and the limit of the sum as 
. 
A) Sum =
; limit of sum as 
is 
B) Sum =
; limit of sum as 
is 
C) Sum =
; limit of sum as 
is 
D) Sum =
; limit of sum as 
is 
. A) Sum =
; limit of sum as is B) Sum =
; limit of sum as is C) Sum =
; limit of sum as is D) Sum =
; limit of sum as is سؤال
Compute the sum of the form 
for the given function and 
-values, with 
equal to the difference in adjacent 
's. 
; 
A)
B)
C)
D)
for the given function and -values, with equal to the difference in adjacent 's. ; A)
B)
C)
D)
سؤال
Translate the following calculation into summation notation and then compute the sum. The sum of the squares of the first 
positive integers.
A)
B)
C)
D)
sum = 
positive integers.A)
B)
C)
D)
sum = سؤال
Write out all terms and compute the sum. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Use summation rules to compute the sum. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Translate the following calculation into summation notation and then compute the sum. Round to two decimal places. The square root of the sum of the first 
positive integers.
A)
sum = 
B)
sum = 
C)
D)
positive integers.A)
sum = B)
sum = C)
D)
سؤال
Suppose that a runner has velocity 
mph for 
minutes, velocity 
mph for 
minutes, velocity 
mph for 
minutes, and velocity 
mph for 
minutes. Find the distance run. Round to two decimal places.
A)
miles
B)
miles
C)
miles
D)
miles
mph for minutes, velocity mph for minutes, velocity mph for minutes, and velocity mph for minutes. Find the distance run. Round to two decimal places.A)
milesB)
milesC)
milesD)
miles سؤال
Suppose that a car has velocity 
mph for 
hours, velocity 
mph for 
hours, velocity 
mph for 
minutes, and velocity 
mph for 
hours. Find the distance traveled. Round to two decimal places.
A)
miles
B)
miles
C)
miles
D)
miles
mph for hours, velocity mph for hours, velocity mph for minutes, and velocity mph for hours. Find the distance traveled. Round to two decimal places.A)
milesB)
milesC)
milesD)
miles سؤال
The table shows the velocity of a projectile at various times. Estimate the distance traveled. Round to two decimal places. 
سؤال
Compute the sum of the form 
for the given function and 
-values, with 
equal to the difference in adjacent 
's. 
; 
A)
B)
C)
D)
for the given function and -values, with equal to the difference in adjacent 's. ; A)
B)
C)
D)
سؤال
List the evaluation points corresponding to the midpoint of each subinterval, sketch the function and corresponding approximating rectangles and evaluate the corresponding Riemann sum. Round the sum to two decimal places. 
سؤال
Approximate the area under the curve on the given interval using 
rectangles and left-endpoint evaluation. Round to three decimal places. 
on 
, 
A)
B)
C)
D)
rectangles and left-endpoint evaluation. Round to three decimal places. on , A)
B)
C)
D)
سؤال
Evaluate the integral by computing the limit of Riemann sums. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Use the Midpoint Rule to estimate the value of the integral (obtain two digits of accuracy). 
A) 1.20
B)
C) 0.77
D) 0.43
A) 1.20
B)
C) 0.77
D) 0.43
سؤال
Approximate the area under the curve on the given interval using 
rectangles and right-endpoint evaluation. Round to three decimal places. 
on 
, 
A)
B)
C)
D)
rectangles and right-endpoint evaluation. Round to three decimal places. on , A)
B)
C)
D)
سؤال
Approximate the area under the curve on the given interval using 
rectangles and right-endpoint evaluation. Round to three decimal places. 
on 
, 
A) 58.704
B) 70.381
C) 63.000
D) 61.698
rectangles and right-endpoint evaluation. Round to three decimal places. on , A) 58.704
B) 70.381
C) 63.000
D) 61.698
سؤال
Use Riemann sums and a limit to compute the exact area under the curve. 
on 
A)
B)
C)
D)
on A)
B)
C)
D)
سؤال
Use the given function values to estimate the area under the curve using left-endpoint and right-endpoint evaluation. Round to two decimal places. 
A) Left-endpoint estimate is
; right-endpoint estimate is 
B) Left-endpoint estimate is
; right-endpoint estimate is 
C) Left-endpoint estimate is
; right-endpoint estimate is 
D) Left-endpoint estimate is
; right-endpoint estimate is 
A) Left-endpoint estimate is
; right-endpoint estimate is B) Left-endpoint estimate is
; right-endpoint estimate is C) Left-endpoint estimate is
; right-endpoint estimate is D) Left-endpoint estimate is
; right-endpoint estimate is سؤال
Use the Midpoint Rule to estimate the value of the integral (obtain two digits of accuracy). 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Approximate the area under the curve on the given interval using 
rectangles and midpoint evaluation. Round to three decimal places. 
on 
, 
A)
B)
C)
D)
rectangles and midpoint evaluation. Round to three decimal places. on , A)
B)
C)
D)
سؤال
Write the given (signed) area as an integral or sum of integrals. The area above the 
-axis and below 
A)
B)
C)
D)
-axis and below A)
B)
C)
D)
سؤال
Approximate the area under the curve on the given interval using 
rectangles and left-endpoint evaluation. Round to three decimal places. 
on 
, 
A)
B)
C)
D)
rectangles and left-endpoint evaluation. Round to three decimal places. on , A)
B)
C)
D)
سؤال
Use Riemann sums and a limit to compute the exact area under the curve. 
on 
on سؤال
Evaluate the integral by computing the limit of Riemann sums. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
List the evaluation points corresponding to the midpoint of each subinterval, and evaluate the corresponding Riemann sum. Round the sum to two decimal places. 
A) Evaluation points:
Riemann sum:
B) Evaluation points:
Riemann sum:
C) Evaluation points:
Riemann sum:
D) Evaluation points:
Riemann sum:
A) Evaluation points:
Riemann sum:
B) Evaluation points:
Riemann sum:
C) Evaluation points:
Riemann sum:
D) Evaluation points:
Riemann sum:
سؤال
Write the given (signed) area as an integral or sum of integrals. The area below the 
-axis and above 
A)
B)
C)
D)
-axis and above A)
B)
C)
D)
سؤال
Approximate the area under the curve on the given interval using 
rectangles and midpoint evaluation. Round to three decimal places. 
on 
, 
A) 1.000
B) 0.020
C) 0.750
D) 0.667
rectangles and midpoint evaluation. Round to three decimal places. on , A) 1.000
B) 0.020
C) 0.750
D) 0.667
سؤال
Give an area interpretation of the integral. 
سؤال
Use Riemann sums and a limit to compute the exact area under the curve. 
on 
A)
B)
C)
D)
on A)
B)
C)
D)
سؤال
Use Riemann sums and a limit to compute the exact area under the curve. 
on 
on سؤال
Use the Integral Mean Value Theorem to estimate the value of the integral. 
سؤال
Compute 
, given 
A)
B)
C)
D)
, given A)
B)
C)
D)
سؤال
Write the given (total) area as an integral or sum of integrals. The area between 
and the 
-axis for 
.
A)
B)
C)
D)
and the -axis for .A)
B)
C)
D)
سؤال
Suppose that, for a particular population of organisms, the birth rate is given by 
organisms per month and the death rate is given by 
organisms per month. Explain why 
represents the net change in population in the first 12 months. Determine for which values of 
it is true that 
. At which times is the population increasing? Decreasing? Determine the time at which the population reaches a maximum.
organisms per month and the death rate is given by organisms per month. Explain why represents the net change in population in the first 12 months. Determine for which values of it is true that . At which times is the population increasing? Decreasing? Determine the time at which the population reaches a maximum. سؤال
Compute the average value of the function on the given interval. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Use the Integral Mean Value Theorem to estimate the value of the integral. 
سؤال
Use the graph to determine whether 
is positive or negative. 
A) Positive
B) Negative
is positive or negative. A) Positive
B) Negative
سؤال
Use Part I of the Fundamental Theorem of Calculus to compute the integral exactly. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Find a value of 
that satisfies the conclusion of the Integral Mean Value Theorem. 
A)
B)
C)
D)
that satisfies the conclusion of the Integral Mean Value Theorem. A)
B)
C)
D)
سؤال
Find a value of 
that satisfies the conclusion of the Integral Mean Value Theorem. 
A)
B)
C)
D)
that satisfies the conclusion of the Integral Mean Value Theorem. A)
B)
C)
D)
سؤال
Write the given (total) area as an integral or sum of integrals. The area between 
and the 
-axis for 
.
A)
B)
C)
D)
and the -axis for .A)
B)
C)
D)
سؤال
Write the expression as a single integral. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Write the expression as a single integral. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Use the graph to determine whether 
is positive or negative. 
A) Positive
B) Negative
is positive or negative. A) Positive
B) Negative
سؤال
Use the given velocity function and initial position to estimate the final position 
. Round to two decimal places. 
A)
B)
C)
D)
. Round to two decimal places. A)
B)
C)
D)
سؤال
Use the graph to determine whether 
is positive or negative. 
A) Positive
B) Negative
is positive or negative. A) Positive
B) Negative
سؤال
Use the given velocity function and initial position to estimate the final position 
. Round to two decimal places. 
A)
B)
C)
D)
. Round to two decimal places. A)
B)
C)
D)
سؤال
Compute the average value of the function on the given interval. 
A)
B)
C)
D)
A)
B)
C)
D)
سؤال
Sketch the area corresponding to the integral. 
سؤال
The impulse-momentum equation states the relationship between a force 
applied to an object of mass 
and the resulting change in velocity 
of the object. The equation is 
, where 
. Suppose that the force of a golf club on a ball is approximately 
thousand pounds for 
between 0 and 
seconds. Using 
slugs for the mass of a golf ball, estimate the change in velocity 
(in ft/s). Round to 2 decimal places.
A)
ft/s
B)
ft/s
C)
ft/s
D)
ft/s
applied to an object of mass and the resulting change in velocity of the object. The equation is , where . Suppose that the force of a golf club on a ball is approximately thousand pounds for between 0 and seconds. Using slugs for the mass of a golf ball, estimate the change in velocity (in ft/s). Round to 2 decimal places.A)
ft/sB)
ft/sC)
ft/sD)
ft/s
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العب
ملء الشاشة (f)
Deck 5: Integration
1
Find the function satisfying the given conditions.
A)
B)
C)
D)
satisfying the given conditions. A)
B)
C)
D)
C
2
Suppose that a car can accelerate from mph to mph in seconds. Assuming a constant acceleration, find the acceleration (in miles per second squared) of the car and find the distance traveled by the car during the seconds.
A) Acceleration = m/s22; distance = miles
B) Acceleration = m/s22; distance = miles
C) Acceleration = m/s22; distance = miles
D) Acceleration = m/s22; distance = miles
mph to mph in seconds. Assuming a constant acceleration, find the acceleration (in miles per second squared) of the car and find the distance traveled by the car during the seconds.A) Acceleration =
m/s22; distance = milesB) Acceleration =
m/s22; distance = milesC) Acceleration =
m/s22; distance = milesD) Acceleration =
m/s22; distance = milesC
3
Suppose that a car can come to rest from mph in seconds. Assuming a constant (negative) acceleration, find the acceleration (in miles per second squared) of the car and find the distance traveled by the car during the seconds (i.e., the stopping distance).
A) Acceleration = m/s2; distance = miles
B) Acceleration = m/s2; distance = miles
C) Acceleration = m/s2; distance = miles
D) Acceleration = m/s2; distance = miles
mph in seconds. Assuming a constant (negative) acceleration, find the acceleration (in miles per second squared) of the car and find the distance traveled by the car during the seconds (i.e., the stopping distance).A) Acceleration =
m/s2; distance = milesB) Acceleration =
m/s2; distance = milesC) Acceleration =
m/s2; distance = milesD) Acceleration =
m/s2; distance = milesB
4
Find the general antiderivative.
A)
B)
C)
D)
A)
B)
C)
D)
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5
Find the function satisfying the given conditions.
A)
B)
C)
D)
satisfying the given conditions. A)
B)
C)
D)
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6
Find all functions satisfying the given conditions.
A)
B)
C)
D)
A)
B)
C)
D)
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7
Find the general antiderivative.
A)
B)
C)
D)
A)
B)
C)
D)
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8
Find an antiderivative by reversing the chain rule, product rule or quotient rule.
A)
B)
C)
D)
A)
B)
C)
D)
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9
Find the general antiderivative.
A)
B)
C)
D)
A)
B)
C)
D)
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10
Determine the position function if the velocity function is and the initial position is .
A)
B)
C)
D)
and the initial position is .A)
B)
C)
D)
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11
Find an antiderivative by reversing the chain rule, product rule or quotient rule.
A)
B)
C)
D)
A)
B)
C)
D)
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12
Sketch a graph of a function corresponding to the given graph of .
corresponding to the given graph of . فتح الحزمة
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13
Determine the position function if the acceleration function is , the initial velocity is , and the initial position is .
A)
B)
C)
D)
, the initial velocity is , and the initial position is .A)
B)
C)
D)
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14
Find all functions satisfying the given conditions.
A)
B)
C)
D)
A)
B)
C)
D)
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15
Sketch a graph of a function corresponding to the given graph of .
corresponding to the given graph of . فتح الحزمة
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16
The following table shows the velocity of a falling object at different times. For each time interval, estimate the distance fallen and the acceleration. Round to two decimal places.
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17
Find an antiderivative by reversing the chain rule, product rule, or quotient rule.
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18
Find the general antiderivative.
A)
B)
C)
D)
A)
B)
C)
D)
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19
Find the general antiderivative.
A)
B)
C)
D)
A)
B)
C)
D)
فتح الحزمة
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20
Find the general antiderivative.
A)
B)
C)
D)
A)
B)
C)
D)
فتح الحزمة
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21
Translate into summation notation.
A)
B)
C)
D)
A)
B)
C)
D)
فتح الحزمة
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22
Use summation rules to compute the sum.
A) 2264
B) 30,784
C) 39,964
D) 2804
A) 2264
B) 30,784
C) 39,964
D) 2804
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23
Use formulas to compute the sum.
A)
B)
C)
D)
A)
B)
C)
D)
فتح الحزمة
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24
Write out all terms and compute the sum.
A)
B)
C)
D)
A)
B)
C)
D)
فتح الحزمة
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25
Use summation rules to compute the sum.
A)
B)
C)
D)
A)
B)
C)
D)
فتح الحزمة
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26
Compute the sum and the limit of the sum as .
A) Sum = ; limit of sum as is
B) Sum = ; limit of sum as is
C) Sum = ; limit of sum as is
D) Sum = ; limit of sum as is
. A) Sum =
; limit of sum as is B) Sum =
; limit of sum as is C) Sum =
; limit of sum as is D) Sum =
; limit of sum as is فتح الحزمة
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27
Use mathematical induction to prove that for all integers .
for all integers . فتح الحزمة
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28
List the evaluation points corresponding to the midpoint of each subinterval, and evaluate the corresponding Riemann sum. Round the sum to two decimal places.
A) Evaluation points:
Riemann sum:
B) Evaluation points:
Riemann sum:
C) Evaluation points:
Riemann sum:
D) Evaluation points:
Riemann sum:
A) Evaluation points:
Riemann sum:
B) Evaluation points:
Riemann sum:
C) Evaluation points:
Riemann sum:
D) Evaluation points:
Riemann sum:
فتح الحزمة
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29
Use summation rules to compute the sum.
A)
B)
C)
D)
A)
B)
C)
D)
فتح الحزمة
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30
The following table shows the acceleration of a car moving in a straight line. If the car is traveling ft/s at time , estimate the speed and distance traveled at each time.
ft/s at time , estimate the speed and distance traveled at each time. فتح الحزمة
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31
Compute the sum and the limit of the sum as .
A) Sum = ; limit of sum as is
B) Sum = ; limit of sum as is
C) Sum = ; limit of sum as is
D) Sum = ; limit of sum as is
. A) Sum =
; limit of sum as is B) Sum =
; limit of sum as is C) Sum =
; limit of sum as is D) Sum =
; limit of sum as is فتح الحزمة
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32
Compute the sum of the form for the given function and -values, with equal to the difference in adjacent 's. ;
A)
B)
C)
D)
for the given function and -values, with equal to the difference in adjacent 's. ; A)
B)
C)
D)
فتح الحزمة
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33
Translate the following calculation into summation notation and then compute the sum. The sum of the squares of the first positive integers.
A)
B)
C)
D) sum =
positive integers.A)
B)
C)
D)
sum = فتح الحزمة
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34
Write out all terms and compute the sum.
A)
B)
C)
D)
A)
B)
C)
D)
فتح الحزمة
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35
Use summation rules to compute the sum.
A)
B)
C)
D)
A)
B)
C)
D)
فتح الحزمة
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36
Translate the following calculation into summation notation and then compute the sum. Round to two decimal places. The square root of the sum of the first positive integers.
A) sum =
B) sum =
C)
D)
positive integers.A)
sum = B)
sum = C)
D)
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37
Suppose that a runner has velocity mph for minutes, velocity mph for minutes, velocity mph for minutes, and velocity mph for minutes. Find the distance run. Round to two decimal places.
A) miles
B) miles
C) miles
D) miles
mph for minutes, velocity mph for minutes, velocity mph for minutes, and velocity mph for minutes. Find the distance run. Round to two decimal places.A)
milesB)
milesC)
milesD)
miles فتح الحزمة
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38
Suppose that a car has velocity mph for hours, velocity mph for hours, velocity mph for minutes, and velocity mph for hours. Find the distance traveled. Round to two decimal places.
A) miles
B) miles
C) miles
D) miles
mph for hours, velocity mph for hours, velocity mph for minutes, and velocity mph for hours. Find the distance traveled. Round to two decimal places.A)
milesB)
milesC)
milesD)
miles فتح الحزمة
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39
The table shows the velocity of a projectile at various times. Estimate the distance traveled. Round to two decimal places.
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40
Compute the sum of the form for the given function and -values, with equal to the difference in adjacent 's. ;
A)
B)
C)
D)
for the given function and -values, with equal to the difference in adjacent 's. ; A)
B)
C)
D)
فتح الحزمة
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41
List the evaluation points corresponding to the midpoint of each subinterval, sketch the function and corresponding approximating rectangles and evaluate the corresponding Riemann sum. Round the sum to two decimal places.
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42
Approximate the area under the curve on the given interval using rectangles and left-endpoint evaluation. Round to three decimal places. on ,
A)
B)
C)
D)
rectangles and left-endpoint evaluation. Round to three decimal places. on , A)
B)
C)
D)
فتح الحزمة
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43
Evaluate the integral by computing the limit of Riemann sums.
A)
B)
C)
D)
A)
B)
C)
D)
فتح الحزمة
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44
Use the Midpoint Rule to estimate the value of the integral (obtain two digits of accuracy).
A) 1.20
B)
C) 0.77
D) 0.43
A) 1.20
B)
C) 0.77
D) 0.43
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45
Approximate the area under the curve on the given interval using rectangles and right-endpoint evaluation. Round to three decimal places. on ,
A)
B)
C)
D)
rectangles and right-endpoint evaluation. Round to three decimal places. on , A)
B)
C)
D)
فتح الحزمة
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46
Approximate the area under the curve on the given interval using rectangles and right-endpoint evaluation. Round to three decimal places. on ,
A) 58.704
B) 70.381
C) 63.000
D) 61.698
rectangles and right-endpoint evaluation. Round to three decimal places. on , A) 58.704
B) 70.381
C) 63.000
D) 61.698
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47
Use Riemann sums and a limit to compute the exact area under the curve. on
A)
B)
C)
D)
on A)
B)
C)
D)
فتح الحزمة
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48
Use the given function values to estimate the area under the curve using left-endpoint and right-endpoint evaluation. Round to two decimal places.
A) Left-endpoint estimate is ; right-endpoint estimate is
B) Left-endpoint estimate is ; right-endpoint estimate is
C) Left-endpoint estimate is ; right-endpoint estimate is
D) Left-endpoint estimate is ; right-endpoint estimate is
A) Left-endpoint estimate is
; right-endpoint estimate is B) Left-endpoint estimate is
; right-endpoint estimate is C) Left-endpoint estimate is
; right-endpoint estimate is D) Left-endpoint estimate is
; right-endpoint estimate is فتح الحزمة
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49
Use the Midpoint Rule to estimate the value of the integral (obtain two digits of accuracy).
A)
B)
C)
D)
A)
B)
C)
D)
فتح الحزمة
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50
Approximate the area under the curve on the given interval using rectangles and midpoint evaluation. Round to three decimal places. on ,
A)
B)
C)
D)
rectangles and midpoint evaluation. Round to three decimal places. on , A)
B)
C)
D)
فتح الحزمة
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51
Write the given (signed) area as an integral or sum of integrals. The area above the -axis and below
A)
B)
C)
D)
-axis and below A)
B)
C)
D)
فتح الحزمة
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52
Approximate the area under the curve on the given interval using rectangles and left-endpoint evaluation. Round to three decimal places. on ,
A)
B)
C)
D)
rectangles and left-endpoint evaluation. Round to three decimal places. on , A)
B)
C)
D)
فتح الحزمة
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53
Use Riemann sums and a limit to compute the exact area under the curve. on
on فتح الحزمة
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54
Evaluate the integral by computing the limit of Riemann sums.
A)
B)
C)
D)
A)
B)
C)
D)
فتح الحزمة
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55
List the evaluation points corresponding to the midpoint of each subinterval, and evaluate the corresponding Riemann sum. Round the sum to two decimal places.
A) Evaluation points:
Riemann sum:
B) Evaluation points:
Riemann sum:
C) Evaluation points:
Riemann sum:
D) Evaluation points:
Riemann sum:
A) Evaluation points:
Riemann sum:
B) Evaluation points:
Riemann sum:
C) Evaluation points:
Riemann sum:
D) Evaluation points:
Riemann sum:
فتح الحزمة
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56
Write the given (signed) area as an integral or sum of integrals. The area below the -axis and above
A)
B)
C)
D)
-axis and above A)
B)
C)
D)
فتح الحزمة
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57
Approximate the area under the curve on the given interval using rectangles and midpoint evaluation. Round to three decimal places. on ,
A) 1.000
B) 0.020
C) 0.750
D) 0.667
rectangles and midpoint evaluation. Round to three decimal places. on , A) 1.000
B) 0.020
C) 0.750
D) 0.667
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58
Give an area interpretation of the integral.
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59
Use Riemann sums and a limit to compute the exact area under the curve. on
A)
B)
C)
D)
on A)
B)
C)
D)
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60
Use Riemann sums and a limit to compute the exact area under the curve. on
on فتح الحزمة
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61
Use the Integral Mean Value Theorem to estimate the value of the integral.
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62
Compute , given
A)
B)
C)
D)
, given A)
B)
C)
D)
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63
Write the given (total) area as an integral or sum of integrals. The area between and the -axis for .
A)
B)
C)
D)
and the -axis for .A)
B)
C)
D)
فتح الحزمة
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64
Suppose that, for a particular population of organisms, the birth rate is given by organisms per month and the death rate is given by organisms per month. Explain why represents the net change in population in the first 12 months. Determine for which values of it is true that . At which times is the population increasing? Decreasing? Determine the time at which the population reaches a maximum.
organisms per month and the death rate is given by organisms per month. Explain why represents the net change in population in the first 12 months. Determine for which values of it is true that . At which times is the population increasing? Decreasing? Determine the time at which the population reaches a maximum. فتح الحزمة
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65
Compute the average value of the function on the given interval.
A)
B)
C)
D)
A)
B)
C)
D)
فتح الحزمة
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66
Use the Integral Mean Value Theorem to estimate the value of the integral.
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67
Use the graph to determine whether is positive or negative.
A) Positive
B) Negative
is positive or negative. A) Positive
B) Negative
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68
Use Part I of the Fundamental Theorem of Calculus to compute the integral exactly.
A)
B)
C)
D)
A)
B)
C)
D)
فتح الحزمة
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69
Find a value of that satisfies the conclusion of the Integral Mean Value Theorem.
A)
B)
C)
D)
that satisfies the conclusion of the Integral Mean Value Theorem. A)
B)
C)
D)
فتح الحزمة
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70
Find a value of that satisfies the conclusion of the Integral Mean Value Theorem.
A)
B)
C)
D)
that satisfies the conclusion of the Integral Mean Value Theorem. A)
B)
C)
D)
فتح الحزمة
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71
Write the given (total) area as an integral or sum of integrals. The area between and the -axis for .
A)
B)
C)
D)
and the -axis for .A)
B)
C)
D)
فتح الحزمة
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72
Write the expression as a single integral.
A)
B)
C)
D)
A)
B)
C)
D)
فتح الحزمة
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73
Write the expression as a single integral.
A)
B)
C)
D)
A)
B)
C)
D)
فتح الحزمة
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74
Use the graph to determine whether is positive or negative.
A) Positive
B) Negative
is positive or negative. A) Positive
B) Negative
فتح الحزمة
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75
Use the given velocity function and initial position to estimate the final position . Round to two decimal places.
A)
B)
C)
D)
. Round to two decimal places. A)
B)
C)
D)
فتح الحزمة
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76
Use the graph to determine whether is positive or negative.
A) Positive
B) Negative
is positive or negative. A) Positive
B) Negative
فتح الحزمة
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77
Use the given velocity function and initial position to estimate the final position . Round to two decimal places.
A)
B)
C)
D)
. Round to two decimal places. A)
B)
C)
D)
فتح الحزمة
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78
Compute the average value of the function on the given interval.
A)
B)
C)
D)
A)
B)
C)
D)
فتح الحزمة
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79
Sketch the area corresponding to the integral.
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80
The impulse-momentum equation states the relationship between a force applied to an object of mass and the resulting change in velocity of the object. The equation is , where . Suppose that the force of a golf club on a ball is approximately thousand pounds for between 0 and seconds. Using slugs for the mass of a golf ball, estimate the change in velocity (in ft/s). Round to 2 decimal places.
A) ft/s
B) ft/s
C) ft/s
D) ft/s
applied to an object of mass and the resulting change in velocity of the object. The equation is , where . Suppose that the force of a golf club on a ball is approximately thousand pounds for between 0 and seconds. Using slugs for the mass of a golf ball, estimate the change in velocity (in ft/s). Round to 2 decimal places.A)
ft/sB)
ft/sC)
ft/sD)
ft/s فتح الحزمة
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k this deck
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 154 في هذه المجموعة.
