Deck 1: Functions and Limits

Question 1

For what value of the constant c is the function f continuous on

A)
B)
C)
D)
E)

Answer 1

Question 2

Find the interval(s) where is continuous.

Answer 2

Question 3

Determine where f is discontinuous.

A)
B)
C)
D)
E)

Answer 3

Question 4

Define the function at 0 so as to make it continuous at 0.

A)
B)
C)
D)

Question 5

How would you define in order to make f continuous at ?

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

Question 6

If f and g are continuous functions with

A)
B)
C)
D)
E)

Question 7

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

Question 8

Use continuity to evaluate the limit.

A)
B)0
C)
D)1
E)

Question 9

Find the limit .

Question 10

For x = 5, determine whether f is continuous from the right, from the left, or neither.

Question 11

Use the graph to determine where the function is discontinuous.

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

Question 12

Find a function g that agrees with f for and is continuous on .

Question 13

Let Find the value of k that will make f continuous on

A)3
B)28
C)-2
D)6

Question 14

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

Question 15

Find the interval(s) where is continuous.

A)
B)
C)
D)

Question 16

Find the limit .

Question 17

Use continuity to evaluate the limit.

Question 18

Choose an equation from the following that expresses the fact that a function is continuous at the number .

A)
B)
C)
D)
E)

Question 19

If a rock is thrown upward on the planet Mars with a velocity of 10 m/s, its height in meters t seconds later is given by . Find the average velocity over the time interval .

A)
B)
C)
D)
E)

Question 20

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

A)5
B)-8
C)
D)-2

Question 21

Evaluate the limit, if it exists.

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

Question 22

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

Question 23

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

Question 24

Sketch the graph of the function f and evaluate

A) 3
B) Does not exist
C) Does not exist
D) 0

Question 25

Find a number such that if , then , where .

Question 26

Use the precise definition of a limit to prove that

Question 27

Use the graph of to guess at the limit , if it exists.

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

Question 28

Sketch the graph of the function f and evaluate

A) 3
B) -1
C) 3
D) -1

Question 29

Use the precise definition of a limit to prove that

Question 30

Find the interval(s) where is continuous.

Question 31

Use a graph to find a number such that whenever .

Question 32

A machinist is required to manufacture a circular metal disk with area 1000 . 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 your answer to the nearest hundred thousandth.

A)
B)
C)
D)
E)

Question 33

The symbol can be used to denote the greatest integer function, which is defined by the greatest integer n such that Use the graph of the function to find the indicated limit, if it exists.

A)0
B)1
C)-0.7
D)0.7

Question 34

Find the limit .

A)5
B)
C)
D)

Question 35

You are given and a tolerance Find a number such that whenever

A)0.04
B)0.0025
C)0.03
D)0.01

Question 36

Use the graph of to guess at the limit , if it exists.

A)1.3
B)0.8
C)0.2
D)Does not exist

Question 37

Find the limit .

A)-2
B)2
C)-4
D)4

Question 38

Is there a number a such that exists? If so, find the value of a and the value of the limit.

A) , limit equals
B) , limit equals
C) , limit equals
D) , limit equals
E) , limit equals

Question 39

You are given that , , and . Find the limit .

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

Question 40

Find the limit , if it exists.

A)2
B)3
C)5
D)Does not exist

Question 41

Find the limit.

A)
B)
C)
D)
E)

Question 42

Evaluate the limit.

Question 43

Evaluate the limit.

A)
B)
C)
D)
E)

Question 44

Find the vertical asymptotes of the function.

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

Question 45

Find the limit.

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

Question 46

Find the limit.

A)
B)
C)
D)
E)

Question 47

Find the limit , if it exists.

A)
B)Does not exist
C)
D)

Question 48

Find the value of . .

A)
B)
C)
D)
E)

Question 49

Evaluate the limit.

Question 50

Find the limit.

Question 51

Let . Find the following limits.

A)
B)
C)
D)
E)

Question 52

If , then if exists, find the value where it exists.

A)
B)1
C)
D)
E)

Question 53

Evaluate the limit.

Question 54

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

Question 55

Estimate the value of the limit by graphing the function . State your answer correct to two decimal places.

A)
B)
C)
D)
E)

Question 56

Use the graph of the function to state the value of , if it exist.

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

Question 57

Use the graph of the function to state the value of , if it exists.

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

Question 58

Evaluate the limit.

Question 59

If , then if exists, to what value does it converge?

A)
B)
C)
D)
E)

Question 60

Given that , and , evaluate the limit.

Question 61

Evaluate the function at the given numbers (correct to six decimal places). Use the results to guess the value of the limit

A)
B)
C)
D)
E)

Question 62

Sketch the graph of over one period.

A)
B)
C)
D)

Question 63

Use the graph of the function to find each limit. , ,

Question 64

The position of a car is given by the values in the following table. (seconds) 0
1
2
3
4 (meters)
0
21)7
26)8
62)4
86)5
Find the average velocity for the time period beginning when and lasting 2 seconds.

A) ft/s
B) ft/s
C)29.85 ft/s
D)33.5 ft/s
E) ft/s

Question 65

The displacement (in feet) of a certain particle moving in a straight line is given by where t is measured in seconds. Find the average velocity over the interval Round your answer to three decimal places.

Question 66

Find the value of the limit.

A)
B)
C)
D)
E)

Question 67

Find the limit.

Question 68

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

Question 69

Use the graph of the function to find each limit. , ,

Question 70

If a rock is thrown upward on the planet Mars with a velocity of , its height in meters t seconds later is given by . Find the average velocity over the time interval .

A) m/s
B) m/s
C) m/s
D) m/s
E) m/s

Question 71

Find the vertical asymptotes of the function.

Question 72

Graph the function by hand, not by plotting points, but by starting with the graph of one of the standard functions and then applying the appropriate transformations.

A)
B)
C)
D)

Question 73

If a ball is thrown into the air with a velocity of , its height (in feet) after t seconds is given by . Find the velocity when

A) ft/s
B) ft/s
C) ft/s
D) ft/s
E) ft/s

Question 74

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

Question 75

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

Question 76

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 77

A tank holds gallons of water, which drains from the bottom of the tank in half an hour. The values in the table show the volume V of water remaining in the tank (in gallons) after minutes. If is the point on the graph of , fill the table with the slopes of the secant lines where Q is the point on the graph with the corresponding . Enter your answer to two decimal places.
t
Slope
5
10
20
25
30

Question 78

The point lies on the curve . If is the point Q , use your calculator to find the slope of the secant line PQ (correct to six decimal places) for the value

A)
B)
C)
D)
E)

Question 79

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 80

By graphing the function and zooming in toward the point where the graph crosses the y-axis, estimate the value of