تكلم مع الذكاء الاصطناعي
Deck 10: An Introduction to Calculus: Limits, Derivatives, and Integrals
ملء الشاشة (f)
سؤال
(a) Explain why direct substitution cannot be used to find the limit
(b) Find the limit algebraically, if it exists.
سؤال
What is the derivative of 
سؤال
Find the instantaneous rate of change of 
at x=3 .
at x=3 . سؤال
Determine the following limits, if they exist.
(a)
(b)
(c)
(d)
(e)
(f)
(a)
(b)
(c)
(d)
(e)
(f)
سؤال
سؤال
Determine 
if the limit exists.
A) -1
B)
C)
D) 1
E) The limit does not exist.
if the limit exists.
A) -1
B)
C)
D) 1
E) The limit does not exist.
سؤال
What is the instantaneous rate of change of 
at x=1 ?
A) 2
B) 0
C) 4
D) 1
at x=1 ?A) 2
B) 0
C) 4
D) 1
سؤال
For the function 
(a) Find the slope of the function at x=1 using the definition of the derivative.
(b) What is the equation of the tangent line to the curve f(x) at x=1 ?
(a) Find the slope of the function at x=1 using the definition of the derivative.
(b) What is the equation of the tangent line to the curve f(x) at x=1 ?
سؤال
The following table lists the population statistics for a certain city.
What is the average rate of change in the population with respect to time between 1975 and 2005 ?
What is the average rate of change in the population with respect to time between 1975 and 2005 ?
سؤال
سؤال
Write the integral that would be used to find the shaded area on the graph shown below.
سؤال
What is the average rate of change of ![What is the average rate of change of over the interval [1.9,2.1] ?<div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB34225555/11ec76bb_394e_57a8_9208_bdba5a858983_TB34225555_11.jpg)
over the interval [1.9,2.1] ?
over the interval [1.9,2.1] ? سؤال
Use the graph below to find the limits or explain why the limits do not exist.
(a)
(b)
(c)
(a)
(b)
(c)
سؤال
Compute the integral 
by computing a geometric area. (Hint: Graph the function first.)
by computing a geometric area. (Hint: Graph the function first.) سؤال
سؤال
Draw the graph of ![Draw the graph of over the interval [0,4] . On the graph, show and shade the rectangles that would be used to approximate the area under the curve by the right rectangle approximation method using 4 subintervals.<div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB34225555/11ec76bc_2e4f_bf5b_9208_e91d7a20e44a_TB34225555_11.jpg)
over the interval [0,4] .
![Draw the graph of over the interval [0,4] . On the graph, show and shade the rectangles that would be used to approximate the area under the curve by the right rectangle approximation method using 4 subintervals.<div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB34225555/11ec76bc_2e51_45fc_9208_e3b867264b95_TB34225555_11.jpg)
On the graph, show and shade the rectangles that would be used to approximate the area under the curve by the right rectangle approximation method using 4 subintervals.
over the interval [0,4] .On the graph, show and shade the rectangles that would be used to approximate the area under the curve by the right rectangle approximation method using 4 subintervals.
سؤال
Draw the graph of f(x)=-2(x-1)(x-4) over the interval [1,4] . On the graph, show and shade the rectangles that would be used to approximate the area under the curve f(x) over [1,4] by the right rectangle approximation method using 6 subintervals. Compute the estimation.
![Draw the graph of f(x)=-2(x-1)(x-4) over the interval [1,4] . On the graph, show and shade the rectangles that would be used to approximate the area under the curve f(x) over [1,4] by the right rectangle approximation method using 6 subintervals. Compute the estimation. <div style=padding-top: 35px>](https://d2lvgg3v3hfg70.cloudfront.net/TB34225555/11ec76c0_158c_f349_9208_234721518f76_TB34225555_11.jpg)
سؤال
At what points c in the domain of 
exist?
exist? سؤال
Find the average rate of change of f(x)=3 \cos x over the interval 
A) -3
B)
C)
D)
A) -3
B)
C)
D)
سؤال
سؤال
سؤال
Explain how to find the area under the graph of 
from x=0 to x=4 by computing the geometric area.
from x=0 to x=4 by computing the geometric area. سؤال
سؤال
Use a calculator to find the RRAM area approximation for the area under the graph 
from x=0 to x=2 with 20 approximating rectangles.
from x=0 to x=2 with 20 approximating rectangles. سؤال
Determine 
if the limit exists.
A) -1
B)
C)
D) 1
E) The limit does not exist.
if the limit exists.
A) -1
B)
C)
D) 1
E) The limit does not exist.
سؤال
For the function 
(a) Find the slope of the function at x=2 using the definition of the derivative.
(b) What is the equation of the tangent line to the curve f(x) at x=2 ?
(a) Find the slope of the function at x=2 using the definition of the derivative.
(b) What is the equation of the tangent line to the curve f(x) at x=2 ?
سؤال
Find the instantaneous rate of change of 
at x=4 .
at x=4 . سؤال
Explain how to find the area under the graph of 
from x=1 to x=5 by computing the geometric area.
from x=1 to x=5 by computing the geometric area. سؤال
Use a calculator to find the LRAM area approximation for the area under the graph 
from x=0 to x=2 with 20 approximating rectangles.
from x=0 to x=2 with 20 approximating rectangles.
سؤال
(a) Explain why direct substitution cannot be used to find the limit.
(b) Find the limit algebraically, if it exists.
سؤال
Determine the following limits, if they exist.
(a)
(b)
(c)
(d)
(e)
(f)
(a)
(b)
(c)
(d)
(e)
(f)
سؤال
Write the integral that would be used to find the shaded area on the graph shown below.
سؤال
At what points c in the domain of f(x) does 
exist?
exist? سؤال
Find the average rate of change of f(x)=5 \tan x over the interval 
A)
B)
C) -10
D) 0
A)
B)
C) -10
D) 0
سؤال
Use the graph below to find the limits or explain why the limits do not exist.
(a)
(b)
(c)
(a)
(b)
(c)
سؤال
سؤال
The following table lists the population statistics for a certain city.
What is the average rate of change in the population with respect to time between 1975 and 2005 ?
What is the average rate of change in the population with respect to time between 1975 and 2005 ?
فتح الحزمة
قم بالتسجيل لفتح البطاقات في هذه المجموعة!
Unlock Deck
Unlock Deck
1/37
العب
ملء الشاشة (f)
Deck 10: An Introduction to Calculus: Limits, Derivatives, and Integrals
1
(a) Explain why direct substitution cannot be used to find the limit
(b) Find the limit algebraically, if it exists.
(a) 
is not defined at x=-4 .
(b) 48
is not defined at x=-4 .(b) 48
2
What is the derivative of
8X
3
Find the instantaneous rate of change of at x=3 .
at x=3 .30
4
Determine the following limits, if they exist.
(a)
(b)
(c)
(d)
(e)
(f)
(a)
(b)
(c)
(d)
(e)
(f)
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 37 في هذه المجموعة.
فتح الحزمة
k this deck
5
A coin is dropped from a window. Find the coin's
(a) average speed during the first 4 sec of fall and
(b) instantaneous speed at t=4 .
(a) average speed during the first 4 sec of fall and
(b) instantaneous speed at t=4 .
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 37 في هذه المجموعة.
فتح الحزمة
k this deck
6
Determine
if the limit exists.
A) -1
B)
C)
D) 1
E) The limit does not exist.
if the limit exists.
A) -1
B)
C)
D) 1
E) The limit does not exist.
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 37 في هذه المجموعة.
فتح الحزمة
k this deck
7
What is the instantaneous rate of change of at x=1 ?
A) 2
B) 0
C) 4
D) 1
at x=1 ?A) 2
B) 0
C) 4
D) 1
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 37 في هذه المجموعة.
فتح الحزمة
k this deck
8
For the function
(a) Find the slope of the function at x=1 using the definition of the derivative.
(b) What is the equation of the tangent line to the curve f(x) at x=1 ?
(a) Find the slope of the function at x=1 using the definition of the derivative.
(b) What is the equation of the tangent line to the curve f(x) at x=1 ?
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 37 في هذه المجموعة.
فتح الحزمة
k this deck
9
The following table lists the population statistics for a certain city.
What is the average rate of change in the population with respect to time between 1975 and 2005 ?
What is the average rate of change in the population with respect to time between 1975 and 2005 ?
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 37 في هذه المجموعة.
فتح الحزمة
k this deck
10
For the function f(x)=4+3 x-2 x2 :
(a) Use the definition of the derivative at a point to find the slope of the tangent line of the function at x=1 .
(b) What is the equation of the tangent line in part a?
(a) Use the definition of the derivative at a point to find the slope of the tangent line of the function at x=1 .
(b) What is the equation of the tangent line in part a?
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 37 في هذه المجموعة.
فتح الحزمة
k this deck
11
Write the integral that would be used to find the shaded area on the graph shown below.
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 37 في هذه المجموعة.
فتح الحزمة
k this deck
12
What is the average rate of change of over the interval [1.9,2.1] ?
over the interval [1.9,2.1] ? فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 37 في هذه المجموعة.
فتح الحزمة
k this deck
13
Use the graph below to find the limits or explain why the limits do not exist.
(a)
(b)
(c)
(a)
(b)
(c)
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 37 في هذه المجموعة.
فتح الحزمة
k this deck
14
Compute the integral by computing a geometric area. (Hint: Graph the function first.)
by computing a geometric area. (Hint: Graph the function first.) فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 37 في هذه المجموعة.
فتح الحزمة
k this deck
15
Find the derivative of f(x)=7 x+10 .
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 37 في هذه المجموعة.
فتح الحزمة
k this deck
16
Draw the graph of over the interval [0,4] .
On the graph, show and shade the rectangles that would be used to approximate the area under the curve by the right rectangle approximation method using 4 subintervals.
over the interval [0,4] .On the graph, show and shade the rectangles that would be used to approximate the area under the curve by the right rectangle approximation method using 4 subintervals.
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 37 في هذه المجموعة.
فتح الحزمة
k this deck
17
Draw the graph of f(x)=-2(x-1)(x-4) over the interval [1,4] . On the graph, show and shade the rectangles that would be used to approximate the area under the curve f(x) over [1,4] by the right rectangle approximation method using 6 subintervals. Compute the estimation.
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 37 في هذه المجموعة.
فتح الحزمة
k this deck
18
At what points c in the domain of exist?
exist? فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 37 في هذه المجموعة.
فتح الحزمة
k this deck
19
Find the average rate of change of f(x)=3 \cos x over the interval
A) -3
B)
C)
D)
A) -3
B)
C)
D)
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 37 في هذه المجموعة.
فتح الحزمة
k this deck
20
Partition the interval [1,5] into eight equal subintervals. List the eight subintervals.
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 37 في هذه المجموعة.
فتح الحزمة
k this deck
21
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 37 في هذه المجموعة.
فتح الحزمة
k this deck
22
Explain how to find the area under the graph of from x=0 to x=4 by computing the geometric area.
from x=0 to x=4 by computing the geometric area. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 37 في هذه المجموعة.
فتح الحزمة
k this deck
23
Find the derivative of f(x)=-4 x-8 .
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 37 في هذه المجموعة.
فتح الحزمة
k this deck
24
Use a calculator to find the RRAM area approximation for the area under the graph from x=0 to x=2 with 20 approximating rectangles.
from x=0 to x=2 with 20 approximating rectangles. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 37 في هذه المجموعة.
فتح الحزمة
k this deck
25
Determine
if the limit exists.
A) -1
B)
C)
D) 1
E) The limit does not exist.
if the limit exists.
A) -1
B)
C)
D) 1
E) The limit does not exist.
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 37 في هذه المجموعة.
فتح الحزمة
k this deck
26
For the function
(a) Find the slope of the function at x=2 using the definition of the derivative.
(b) What is the equation of the tangent line to the curve f(x) at x=2 ?
(a) Find the slope of the function at x=2 using the definition of the derivative.
(b) What is the equation of the tangent line to the curve f(x) at x=2 ?
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 37 في هذه المجموعة.
فتح الحزمة
k this deck
27
Find the instantaneous rate of change of at x=4 .
at x=4 . فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 37 في هذه المجموعة.
فتح الحزمة
k this deck
28
Explain how to find the area under the graph of from x=1 to x=5 by computing the geometric area.
from x=1 to x=5 by computing the geometric area. فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 37 في هذه المجموعة.
فتح الحزمة
k this deck
29
Use a calculator to find the LRAM area approximation for the area under the graph
from x=0 to x=2 with 20 approximating rectangles.
from x=0 to x=2 with 20 approximating rectangles.
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 37 في هذه المجموعة.
فتح الحزمة
k this deck
30
(a) Explain why direct substitution cannot be used to find the limit.
(b) Find the limit algebraically, if it exists.
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 37 في هذه المجموعة.
فتح الحزمة
k this deck
31
Determine the following limits, if they exist.
(a)
(b)
(c)
(d)
(e)
(f)
(a)
(b)
(c)
(d)
(e)
(f)
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 37 في هذه المجموعة.
فتح الحزمة
k this deck
32
Write the integral that would be used to find the shaded area on the graph shown below.
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 37 في هذه المجموعة.
فتح الحزمة
k this deck
33
At what points c in the domain of f(x) does exist?
exist? فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 37 في هذه المجموعة.
فتح الحزمة
k this deck
34
Find the average rate of change of f(x)=5 \tan x over the interval
A)
B)
C) -10
D) 0
A)
B)
C) -10
D) 0
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 37 في هذه المجموعة.
فتح الحزمة
k this deck
35
Use the graph below to find the limits or explain why the limits do not exist.
(a)
(b)
(c)
(a)
(b)
(c)
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 37 في هذه المجموعة.
فتح الحزمة
k this deck
36
A baseball is dropped from a window. Find the baseball's (a) average speed during the first 2 sec of fall and (b) instantaneous speed at t=2 .
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 37 في هذه المجموعة.
فتح الحزمة
k this deck
37
The following table lists the population statistics for a certain city.
What is the average rate of change in the population with respect to time between 1975 and 2005 ?
What is the average rate of change in the population with respect to time between 1975 and 2005 ?
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 37 في هذه المجموعة.
فتح الحزمة
k this deck
فتح الحزمة
افتح القفل للوصول البطاقات البالغ عددها 37 في هذه المجموعة.
