Deck 2: Limits and Derivatives

Question 1

Find the limit.

Answer 1

0

Question 2

You are given the graph of Find the horizontal and vertical asymptotes of the graph of

Answer 2

VA

Question 3

The graph shows the percentage of households in a certain city watching television during a 24-hr period on a weekday corresponds to 6a.m.).By computing the slope of the respective tangent line, estimate the rate of change of the percentage of households watching television at a-12 p.m.Note that

Answer 3

Falling at

Question 4

Use the graph of the function to find each limit.

Question 5

Find the limit

Question 6

Find the limit.

Question 7

Use the precise definition of a limit to prove that

Question 8

Find an equation of the tangent line to the curve.

Question 9

Evaluate the limit.

Question 10

Find the limit.

Question 11

Find the interval(s) where is continuous.

Question 12

How close to do we have to take so that

Question 13

How close to 2 do we have to take x so that is within a distance of 0.01 from 13?

Question 14

Find the derivative of the function and evaluate at the given value of x.

Question 15

Let a.Sketch the graph of
b.For what values of x is f differentiable?
c.Find a formula for

Question 16

Find the numbers, if any, where the function is discontinuous.

Question 17

Find the limit.

Question 18

Find the limit if

Question 19

Complete the table by computing at the given values of accurate to five decimal places.Use the results to guess at the indicated limit, if it exists, to three decimal places.

Question 20

If and are continuous functions with

Question 21

Use the definition of the limit to find values of that corresponds to Round yourAnswer to the nearest thousandth.

Question 22

The position of a car is given by the values in the following table. Estimate the instantaneous velocity when by averaging the velocities for the periods

Question 23

Find the limit.

Question 24

Use the precise definition of a limit to prove that

Question 25

Find an equation of the tangent line to the curve at the point (1, 1).

Question 26

Find the limit.

Question 27

Find the limit.

Question 28

For the function whose graph is shown, state the following.

Question 29

Use continuity to evaluate the limit.

Question 30

Evaluate the limit.

Question 31

Use the graph of the function to find each limit.

Question 32

If a cylindrical tank holds gallons of water, which can be drained from the bottom of the tank in an hour, then Torricelli's Law gives the volume of water remaining in the tank after minutes as Find the rate at which the water is flowing out of the tank (the instantaneous rate of change of with respect to as a function of

Question 33

Consider the following function. Determine the values of a for which exists.

Question 34

Use a graph to find a number such that whenever Round yourAnswer to the nearest thousandth.

Question 35

Evaluate the limit.

Question 36

Let a.Sketch the graph of c.Find a formula for
b.For what values of differentiable?

Question 37

Sketch the graph of the derivative of the function whose graph is given.

Question 38

How close to do we have to take x so that

Question 39

How close to 2 do we have to take x so that is within a distance of 0.01 from 13?

Question 40

Use a graph to find a number such that whenever

Question 41

Select the correct Answer for each question.
The point lies on the curve If is the point use your calculator to find the slope of the secant line (correct to six decimal places) for the value

A)
B)
C)
D)
E)

Question 42

Select the correct Answer for each question.
Use the graph of the function o find the value(s) of at which is not differentiable.

A)- 3
B)
C)- 6
D)3

Question 43

Select the correct Answer for each question.
Suppose the distance s (in feet) covered by a car moving along a straight road after t sec is given by the function Calculate the (instantaneous) velocity of the car when

A)223 ft/sec
B)16 ft/sec
C)560 ft/sec
D)4130 ft/sec

Question 44

Select the correct Answer for each question.
Find the vertical asymptotes of the function.

A)
B)
C)
D)
E)None of these

Question 45

Select the correct Answer for each question.
Let Find the value of k that will make continuous on

A)5
B)46
C)-4
D)3

Question 46

Select the correct Answer for each question.
A machinist is required to manufacture a circular metal disk with area If the machinist is allowed an error tolerance of in the area of the disk, how close to the ideal radius must the machinist control the radius? Round yourAnswer to the nearest hundred thousandth.

A)
B)
C)
D)
E)

Question 47

Select the correct Answer for each question.
Sketch the graph of the function f and evaluate

A)
B)
C)
D) x

Question 48

Select the correct Answer for each question.
Evaluate the limit.

A)
B)
C)
D)
E)

Question 49

Select the correct Answer for each question.
nd g are continuous functions with

A)
B)
C)
D)
E)

Question 50

Select the correct Answer for each question.
Find the limit if it exists.

A)1
B)3
C)2
D)Does not exist

Question 51

Select the correct Answer for each question.
You are given that nd Find the limit

A)17
B)-8
C)0
D)22

Question 52

Select the correct Answer for each question.
Find the horizontal and vertical asymptotes of the graph of the function

A)HA VA
B)HA VA none
C)HA A none HA VA
D)

Question 53

Select the correct Answer for each question.
Use the graph to determine where the function is discontinuous.

A)At 0
B)On the interval
C)At
D)At 1

Question 54

Select the correct Answer for each question.
Find the limit by evaluating the derivative of a suitable function at an appropriate value of x.(Hint: Use the definition of the derivative.)

A)25
B)75
C)
D)

Question 55

Select the correct Answer for each question.
If use the definition of derivative to find

A)
B)
C)
D)
E)None of these

Question 56

Select the correct Answer for each question.
Use the graph of the function to state the value of if it exists.

A)
B)
C)does not exist
D)1
E)

Question 57

Select the correct Answer for each question.
Find the limit.

A)
B)0
C)
D)

Question 58

Select the correct Answer for each question.
Find the limit.

A)0
B)
C)
D)
E)does not exist

Question 59

Select the correct Answer for each question.
Find the numbers, if any, where the function is discontinuous.

A)
B)2
C)1
D)0

Question 60

Select the correct Answer for each question.
If a rock is thrown upward on the planet Mars with a velocity of its height in meters seconds later is given by Find the average velocity over the time interval

A)
B)
C)
D)
E)

Question 61

Select the correct Answer for each question.
Use the graph of to guess at the limit , if it exists.

A)1
B)4
C)3
D)Does not exist

Question 62

Select the correct Answer for each question.
The symbol an be used to denote the greatest integer function, which is defined by the greatest integer such that Use the graph of the function to find the indicated limit, if it exists.

A)0
B)-1
C)-0.3
D)0.3

Question 63

Select the correct Answer for each question.
Sketch the graph of the function nd evaluate

A)
B) x
C)
D)

Question 64

Select the correct Answer for each question.
At what point is the function not differentiable.

A)
B)
C)
D)
E)

Question 65

Select the correct Answer for each question.
Evaluate the limit, if it exists.

A)
B)1
C)
D)
E)does not exist

Question 66

Select the correct Answer for each question.
If

A)
B)
C)
D)
E)does not exist

Question 67

Select the correct Answer for each question.
Find the limit.

A)
B)
C)
D)
E)does not exist

Question 68

Select the correct Answer for each question.
Find the vertical asymptotes of the function.

A)
B)
C)
D)
E)none of these

Question 69

Select the correct Answer for each question.
Use the graph to determine where the function is discontinuous.

A)At 1
B)On the interval
C)At 0
D)At

Question 70

Select the correct Answer for each question.
Evaluate

A)0
B)-2
C)2
D)Undefined

Question 71

Select the correct Answer for each question.
Sketch the graph of the function and evaluate

A)
B)
C)
D)

Question 72

Select the correct Answer for each question.
Find an equation of the tangent line to the curve at the point

A)
B)
C)
D)
E)None of these

Question 73

Select the correct Answer for each question.
The cost (in dollars) of producing x units of a certain commodity is Find the instantaneous rate of change with respect to x when (This is called the marginal cost.)

A)
B)
C)
D)
E)

Question 74

Select the correct Answer for each question.
The cost (in dollars) of producing x units of a certain commodity is Find the average rate of change with respect to when the production level is changed from to

A)
B)
C)
D)
E)

Question 75

Select the correct Answer for each question.
Find the limit.

A)
B)
C)
D)
E)

Question 76

Select the correct Answer for each question.
Let Find the following limits.

A)
B)
C)
D)both
E)both 1

Question 77

Select the correct Answer for each question.
Find the limit if it exists.

A)-2
B)Does not exist
C)3
D)1

Question 78

Select the correct Answer for each question.
For what value of the constant is the function continuous on

A)
B)
C)
D)
E)

Question 79

Select the correct Answer for each question.
Find the horizontal and vertical asymptotes of the graph of the function

A)HA VA
B)HA VA none
C)HA A none HA VA
D)

Question 80

Select the correct Answer for each question.
Find the tangent line to the parabola at the point

A)
B)
C)
D)
E)None of these