Question 1

Use the table to estimate the rate of change of y at the specified value of x.&#10;x = 1.  &#10;A) 0.5&#10;B) 1&#10;C) 2&#10;D) 1.5

Accepted Answer

B

Question 2

Find the average rate of change of the function over the given interval.&#10;

Accepted Answer

The average rate of change of a function over an interval is given by the formula:
average rate of change = (change in y) / (change in x)

In this case, the function is y = 3/(x-2) and the interval is [4,7].

The change in y over the interval is:
y(7) - y(4) = (3/(7-2)) - (3/(4-2)) = -3/10
(Note: We subtract the value of y at the lower endpoint from the value of y at the upper endpoint to get the change in y.)

The change in x over the interval is:
7 - 4 = 3

Therefore, the average rate of change of the function over the interval [4,7] is:
average rate of change = (change in y) / (change in x)
                       = (-3/10) / 3
                       = -3/30
                       = -1/10
Thus, the answer is B, -3/10.

Question 3

Use the slopes of UQ, UR, US, and UT to estimate the rate of change of y at the specified value of x.&#10;x = 3  &#10;A) 2&#10;B) 0&#10;C) 6&#10;D) 4

Accepted Answer

D

Question 4

Find the slope of the curve at the given point P and an equation of the tangent line at P.&#10;

Accepted Answer

To find the slope of the curve at a given point, we differentiate the given function with respect to $x$. The derivative of $y = x^2 + 11x - 15$ is $y' = 2x + 11$. Substituting $x = 1$ into $y'$ gives $2(1) + 11 = 13$, which is the slope at point $1, -3$. To find the equation of the tangent line at $P(1, -3)$, we use the point-slope form: $y - y_1 = m(x - x_1)$, where $m = 13$, $x_1 = 1$, and $y_1 = -3$. Substituting these values gives $y + 3 = 13(x - 1)$, or $y = 13x - 16$.

Question 5

Find the average rate of change of the function over the given interval.&#10;

Accepted Answer

The average rate of change of a function $y = f(x)$ over an interval $[a, b]$ is given by $\frac{f(b) - f(a)}{b - a}$. For $y = \sqrt{2x}$ over the interval $[2, 8]$, we calculate $f(8) = \sqrt{2*8} = \sqrt{16} = 4$ and $f(2) = \sqrt{2*2} = \sqrt{4} = 2$. Thus, the average rate of change is $\frac{4 - 2}{8 - 2} = \frac{2}{6} = \frac{1}{3}$.

Question 6

Use the slopes of UQ, UR, US, and UT to estimate the rate of change of y at the specified value of x.&#10;x = 2  &#10;A) 0&#10;B) 6&#10;C) 4&#10;D) 3

Accepted Answer

The answer of Use the slopes of UQ, UR, US,...

Question 7

Find the average rate of change of the function over the given interval.&#10;

Accepted Answer

The average rate of change of a function $y = f(x)$ over an interval $[a, b]$ is given by $\frac{f(b) - f(a)}{b - a}$. For the given function $y = x^2 + 4x$ and interval $[4, 7]$, we first find $f(4) = 4^2 + 4(4) = 16 + 16 = 32$ and $f(7) = 7^2 + 4(7) = 49 + 28 = 77$. Then, the average rate of change is $\frac{77 - 32}{7 - 4} = \frac{45}{3} = 15$.

Question 8

Use the slopes of UQ, UR, US, and UT to estimate the rate of change of y at the specified value of x.&#10;x = 5  &#10;A) 0&#10;B) 1&#10;C) 5&#10;D) 2

Accepted Answer

The answer of Use the slopes of UQ, UR, US,...

Question 9

Use the table to estimate the rate of change of y at the specified value of x.&#10;x = 1.  &#10;A) 2&#10;B) 1&#10;C) 0.5&#10;D) 1.5

Accepted Answer

The rate of change of y at x = 1 can be estimated using the difference quotient: (y(1.2) - y(1.0)) / (1.2 - 1.0) = (0.36 - 0.25) / (0.2) = 0.11 / 0.2 = 0.55, which is closest to 0.5.

Question 10

Find the average rate of change of the function over the given interval.&#10;

Accepted Answer

The average rate of change of a function $y = f(x)$ over an interval $[a, b]$ is given by $\frac{f(b) - f(a)}{b - a}$. For the given function $y = -3x^2 - x$ over the interval $[5, 6]$, we first find $f(5) = -3(5)^2 - 5 = -75 - 5 = -80$ and $f(6) = -3(6)^2 - 6 = -108 - 6 = -114$. Then, the average rate of change is $\frac{-114 - (-80)}{6 - 5} = \frac{-114 + 80}{1} = \frac{-34}{1} = -34$.

Question 11

Find the average rate of change of the function over the given interval.&#10;

Accepted Answer

The answer of Find the average rate of change of...

Question 12

Find the slope of the curve at the given point P and an equation of the tangent line at P.&#10;

Accepted Answer

The answer of Find the slope of the curve at...

Question 13

Use the slopes of UQ, UR, US, and UT to estimate the rate of change of y at the specified value of x.&#10;x = 2.5  &#10;A) 1.25&#10;B) 3.75&#10;C) 7.5&#10;D) 0

Accepted Answer

The answer of Use the slopes of UQ, UR, US,...

Question 14

Find the average rate of change of the function over the given interval.&#10;

Accepted Answer

The answer of Find the average rate of change of...

Question 15

Find the slope of the curve at the given point P and an equation of the tangent line at P.&#10;

Accepted Answer

The answer of Find the slope of the curve at...

Question 16

Use the slopes of UQ, UR, US, and UT to estimate the rate of change of y at the specified value of x.&#10;x = 5  &#10;A) 254&#10;B) 0&#10;C) 52&#10;D) 54

Accepted Answer

The answer of Use the slopes of UQ, UR, US,...

Question 17

Find the slope of the curve at the given point P and an equation of the tangent line at P.&#10;

Accepted Answer

The answer of Find the slope of the curve at...

Question 18

Find the average rate of change of the function over the given interval.&#10;

Accepted Answer

The answer of Find the average rate of change of...

Question 19

Find the slope of the curve at the given point P and an equation of the tangent line at P.&#10;

Accepted Answer

The answer of Find the slope of the curve at...

Question 20

Find the average rate of change of the function over the given interval.&#10;

Accepted Answer

The answer of Find the average rate of change of...

Question 21

Use the graph to evaluate the limit.&#10;lim f(x) x&#57359;0  &#10;A) does not exist&#10;B)&#10;C) 1&#10;D) -1

Accepted Answer

The answer of Use the graph to evaluate the limit.&#10;lim...

Question 22

Use the table to estimate the rate of change of y at the specified value of x.&#10;x = 1.  &#10;A) 8&#10;B) 6&#10;C) 2&#10;D) 4

Accepted Answer

The answer of Use the table to estimate the rate...

Question 23

Use the table to estimate the rate of change of y at the specified value of x.&#10;x = 2.  &#10;A) 0&#10;B) 8&#10;C) -8&#10;D) 4

Accepted Answer

The answer of Use the table to estimate the rate...

Question 24

lim f(x) x&#57359;0  &#10;A) 1&#10;B) -2&#10;C) 0&#10;D) does not exist

Accepted Answer

The answer of lim f(x) x&#57359;0  &#10;A) 1&#10;B) -2&#10;C)...

Question 25

Use the table to estimate the rate of change of y at the specified value of x.&#10;x = 1.  &#10;A) 0&#10;B) 1&#10;C) 0.5&#10;D) -0.5

Accepted Answer

The answer of Use the table to estimate the rate...

Question 26

lim f(x) x&#57359;0  &#10;A) -2&#10;B) 0&#10;C) 2&#10;D) does not exist

Accepted Answer

The answer of lim f(x) x&#57359;0  &#10;A) -2&#10;B) 0&#10;C)...

Question 27

Find the limit.&#10; &#10;A) does not exist&#10;B) 0&#10;C) -5&#10;D) 5

Accepted Answer

The answer of Find the limit.&#10; &#10;A) does not exist&#10;B)...

Question 28

Use the graph to evaluate the limit.&#10; &#10;A) 2&#10;B) -2&#10;C) does not exist&#10;D) 0

Accepted Answer

The answer of Use the graph to evaluate the limit.&#10;...

Question 29

Use the graph to evaluate the limit.&#10; &#10;A) 1&#10;B) does not exist&#10;C)&#10;D) -1

Accepted Answer

The answer of Use the graph to evaluate the limit.&#10;...

Question 30

Find the limit.&#10; &#10;A) 19&#10;B) -13&#10;C) 11&#10;D) 3

Accepted Answer

The answer of Find the limit.&#10; &#10;A) 19&#10;B) -13&#10;C) 11&#10;D)...

Question 31

Use the table to estimate the rate of change of y at the specified value of x.
When exposed to ethylene gas, green bananas will ripen at an accelerated rate. The number of days for ripening becomes shorter for longer exposure times. Assume that the table below gives average ripening times of
Bananas for several different ethylene exposure times.

Plot the data and then find a line approximating the data. With the aid of this line, determine the rate of change of
Ripening time with respect to exposure time. Round your answer to two significant digits.

38 minutes -0.14 day per minute

Accepted Answer

The answer of Use the table to estimate the rate...

Question 32

The graph below shows the number of tuberculosis deaths in the United States from 1989 to 1998.   Estimate the average rate of change in tuberculosis deaths from 1993 to 1995.&#10;A) About -150 deaths per year&#10;B) About -300 deaths per year&#10;C) About -1 deaths per year&#10;D) About -80 deaths per year

Accepted Answer

The answer of The graph below shows the number of...

Question 33

lim f(x) x&#57359;0  &#10;A) 0&#10;B) -1&#10;C) does not exist&#10;D) 1

Accepted Answer

The answer of lim f(x) x&#57359;0  &#10;A) 0&#10;B) -1&#10;C)...

Question 34

Use the graph to evaluate the limit.&#10; &#10;A) -3&#10;B) 0&#10;C) does not exist&#10;D) 3

Accepted Answer

The answer of Use the graph to evaluate the limit.&#10;...

Question 35

Use the graph to evaluate the limit.&#10;

Accepted Answer

The answer of Use the graph to evaluate the limit.&#10;...

Question 36

lim f(x) x&#57359;0  &#10;A) 2&#10;B) -1&#10;C) does not exist&#10;D) -2

Accepted Answer

The answer of lim f(x) x&#57359;0  &#10;A) 2&#10;B) -1&#10;C)...

Question 37

Use the table to estimate the rate of change of y at the specified value of x.
When exposed to ethylene gas, green bananas will ripen at an accelerated rate. The number of days for ripening becomes shorter for longer exposure times. Assume that the table below gives average ripening times of
Bananas for several different ethylene exposure times.

Plot the data and then find a line approximating the data. With the aid of this line, determine the rate of change of
Ripening time with respect to exposure time. Round your answer to two significant digits.

38 minutes -0.14 day per minute

Accepted Answer

The answer of Use the table to estimate the rate...

Question 38

Find the limit.&#10; &#10;A) does not exist&#10;B) 0&#10;C) 18&#10;D) -18

Accepted Answer

The answer of Find the limit.&#10; &#10;A) does not exist&#10;B)...

Question 39

Use the graph to evaluate the limit.&#10; &#10;A) 6&#10;B) -1&#10;C) does not exist&#10;D) 0

Accepted Answer

The answer of Use the graph to evaluate the limit.&#10;...

Question 40

Find the limit.&#10; &#10;A) -2&#10;B) does not exist&#10;C) 0&#10;D) 2

Accepted Answer

The answer of Find the limit.&#10; &#10;A) -2&#10;B) does not...

Question 41

Find the limit, if it exists.&#10; &#10;A) 14&#10;B) 28&#10;C) Does not exist&#10;D) 0

Accepted Answer

The answer of Find the limit, if it exists.&#10; &#10;A)...

Question 42

Find the limit if it exists.&#10;

Accepted Answer

The answer of Find the limit if it exists.&#10; ...

Question 43

Find the limit if it exists.&#10; &#10;A) -32&#10;B) -76&#10;C) 32&#10;D) 76

Accepted Answer

The answer of Find the limit if it exists.&#10; &#10;A)...

Question 44

Find the limit if it exists.&#10; &#10;A) -225&#10;B) -135&#10;C) -81&#10;D) 135

Accepted Answer

The answer of Find the limit if it exists.&#10; &#10;A)...

Question 45

Find the limit if it exists.&#10;

Accepted Answer

The answer of Find the limit if it exists.&#10; ...

Question 46

Find the limit.&#10; &#10;A) -23&#10;B) 25&#10;C) 121&#10;D) 89

Accepted Answer

The answer of Find the limit.&#10; &#10;A) -23&#10;B) 25&#10;C) 121&#10;D)...

Question 47

Find the limit if it exists.&#10;

Accepted Answer

The answer of Find the limit if it exists.&#10; ...

Question 48

Find the limit.&#10;

Accepted Answer

The answer of Find the limit.&#10;   ...

Question 49

Find the limit, if it exists.&#10;

Accepted Answer

The answer of Find the limit, if it exists.&#10; ...

Question 50

Find the limit, if it exists.&#10;

Accepted Answer

The answer of Find the limit, if it exists.&#10; ...

Question 51

Find the limit, if it exists.&#10;

Accepted Answer

The answer of Find the limit, if it exists.&#10; ...

Question 52

Find the limit if it exists.&#10;

Accepted Answer

The answer of Find the limit if it exists.&#10; ...

Question 53

Find the limit if it exists.&#10;

Accepted Answer

The answer of Find the limit if it exists.&#10; ...

Question 54

Find the limit if it exists.&#10;

Accepted Answer

The answer of Find the limit if it exists.&#10; ...

Question 55

Find the limit if it exists.&#10;

Accepted Answer

The answer of Find the limit if it exists.&#10; ...

Question 56

Find the limit.&#10; &#10;A) 0&#10;B) does not exist&#10;C) 29&#10;D) 15

Accepted Answer

The answer of Find the limit.&#10; &#10;A) 0&#10;B) does not...

Question 57

Find the limit if it exists.&#10; &#10;A) 302&#10;B) 290&#10;C) 350&#10;D) 338

Accepted Answer

The answer of Find the limit if it exists.&#10; &#10;A)...

Question 58

Find the limit.&#10; &#10;A) &#177;10&#10;B) 10&#10;C) 100&#10;D) does not exist

Accepted Answer

The answer of Find the limit.&#10; &#10;A) &#177;10&#10;B) 10&#10;C) 100&#10;D)...

Question 59

Find the limit, if it exists.&#10;

Accepted Answer

The answer of Find the limit, if it exists.&#10; ...

Question 60

Find the limit, if it exists.&#10; &#10;A) 4&#10;B) -4&#10;C) Does not exist&#10;D) 0

Accepted Answer

The answer of Find the limit, if it exists.&#10; &#10;A)...

Question 61

Find the limit, if it exists.&#10;

Accepted Answer

The answer of Find the limit, if it exists.&#10; ...

Question 62

Give an appropriate answer.&#10; &#10;A) 10&#10;B) 70&#10;C) 5&#10;D) 17

Accepted Answer

The answer of Give an appropriate answer.&#10; &#10;A) 10&#10;B) 70&#10;C)...

Question 63

Find the limit, if it exists.&#10;

Accepted Answer

The answer of Find the limit, if it exists.&#10; ...

Question 64

Find the limit, if it exists.&#10;

Accepted Answer

The answer of Find the limit, if it exists.&#10; ...

Deck 2: Limits and Derivatives