Question 1

Given   ,   and   , find   .

Accepted Answer

A)    
B)    
C)    
D)  The limit does not exist. 
A)    
B)    
C)    
D)  The limit does not exist.

Question 2

Determine the limit.   Answer with a number,   ,   or that the limit does not exist.

Accepted Answer

A)    
B)    
C)  0 
D)  9 
E)  The limit does not exist. 
A)    
B)    
C)  0 
D)  9 
E)  The limit does not exist.

Question 3

Find all discontinuities.

Accepted Answer

A)  discontinuous at   
B)  discontinuous at   
C)  discontinuous at   
D)  continuous for all x 
A)  discontinuous at   
B)  discontinuous at   
C)  discontinuous at   
D)  continuous for all x

Question 4

Evaluate the limit, if it exists.

Accepted Answer

A)  0 
B)  1 
C)    
D)  does not exist 
A)  0 
B)  1 
C)    
D)  does not exist

Question 5

Given   and   , find   .

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 6

For the position function f(t)   (feet) find the instantaneous velocity at time   seconds.

Accepted Answer

A)    feet per second 
B)    feet per second 
C)    feet per second 
D)    feet per second 
A)    feet per second 
B)    feet per second 
C)    feet per second 
D)    feet per second

Question 7

For the position function f(t)   (feet) find the instantaneous velocity at time   seconds.

Accepted Answer

A)    feet per second 
B)    feet per second 
C)    feet per second 
D)    feet per second 
A)    feet per second 
B)    feet per second 
C)    feet per second 
D)    feet per second

Question 8

A metal washer of (outer) radius r inches weighs   ounces. A company manufactures 5-inch washers for different customers who have different error tolerances. If the customer demands a washer of weight   ounces, what is the error tolerance for the radius? That is, find   such that a radius of r within the interval   guarantees a weight within   .

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 9

Use the graph to identify all discontinuities of f.

Accepted Answer

The functi

Question 10

Use graphical and numerical evidence to estimate the limit.

Accepted Answer

A)  0 
B)    
C)    
D)    
A)  0 
B)    
C)    
D)

Question 11

Use graphical and numerical evidence to estimate the limit.

Accepted Answer

A)    
B)    
C)    
D)    
A)    
B)    
C)    
D)

Question 12

Prove that the limit is correct using the appropriate definition. Assume k is an integer and is greater than 0. Show all work.

Accepted Answer

The answer of Prove that the limit is correct using...

Question 13

Find   in terms of   for   .

Accepted Answer

A)    
B)  4 
C)    
D)  0 
A)    
B)  4 
C)    
D)  0

Question 14

Use the graph to identify all discontinuities of f.

Accepted Answer

The functi

Question 15

Determine all vertical and slant asymptotes.

Accepted Answer

A)  vertical asymptotes:     slant asymptote:   
B)  vertical asymptote:   slant asymptote:   
C)  vertical asymptote:   slant asymptote:   
D)  vertical asymptotes:     slant asymptote:   
A)  vertical asymptotes:     slant asymptote:   
B)  vertical asymptote:   slant asymptote:   
C)  vertical asymptote:   slant asymptote:   
D)  vertical asymptotes:     slant asymptote:

Question 16

For the function graphed below, identify   or state that the limit does not exist.

Accepted Answer

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

Question 17

Prove that the limit is correct using the appropriate definition. Show all work.

Accepted Answer

The answer of Prove that the limit is correct using...

Question 18

A ski rental shop charges $7.00 for each hour, or portion of an hour, its ski equipment is rented for up to a maximum of $56.00 for all day. If   equals the total charge for the ski equipment for t hours, determine the limit   , if it exists.

Accepted Answer

A)  $45.50 
B)  $42.00 
C)  $49.00 
D)  The limit does not exist. 
A)  $45.50 
B)  $42.00 
C)  $49.00 
D)  The limit does not exist.

Question 19

Use graphical and numerical evidence to determine if   exists. If so, state the limit.

Accepted Answer

A)  the limit exists and is   at   
B)  the limit exists and is 0 at   
C)  does not exist; the right and left limits at   are different 
D)  does not exist; the function is increasing without bound at   
A)  the limit exists and is   at   
B)  the limit exists and is 0 at   
C)  does not exist; the right and left limits at   are different 
D)  does not exist; the function is increasing without bound at

Question 20

Sketch the graph of   . What is   ?

Accepted Answer

A)    
B)  0 
C)  5 
D)  does not exist 
A)    
B)  0 
C)  5 
D)  does not exist

Given , and , find .

Determine the limit. Answer with a number, , or that the limit does not exist.

Find all discontinuities.

Evaluate the limit, if it exists.

Given and , find .

For the position function f(t) (feet) find the instantaneous velocity at time seconds.

For the position function f(t) (feet) find the instantaneous velocity at time seconds.

Use the graph to identify all discontinuities of f.

Use graphical and numerical evidence to estimate the limit.

Use graphical and numerical evidence to estimate the limit.

Prove that the limit is correct using the appropriate definition. Assume k is an integer and is greater than 0. Show all work.

Find in terms of for .

Use the graph to identify all discontinuities of f.

Determine all vertical and slant asymptotes.

For the function graphed below, identify or state that the limit does not exist.

Prove that the limit is correct using the appropriate definition. Show all work.

A ski rental shop charges $7.00 for each hour, or portion of an hour, its ski equipment is rented for up to a maximum of $56.00 for all day. If equals the total charge for the ski equipment for t hours, determine the limit , if it exists.

Use graphical and numerical evidence to determine if exists. If so, state the limit.

Sketch the graph of . What is ?

Preliminaries

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

Integration Techniques

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters

Exam 2: Limits and Continuity

Given , and , find .

Determine the limit. Answer with a number, , or that the limit does not exist.

Find all discontinuities.

Evaluate the limit, if it exists.

Given and , find .

For the position function f(t) (feet) find the instantaneous velocity at time seconds.

For the position function f(t) (feet) find the instantaneous velocity at time seconds.

Use the graph to identify all discontinuities of f.

Use graphical and numerical evidence to estimate the limit.

Use graphical and numerical evidence to estimate the limit.

Prove that the limit is correct using the appropriate definition. Assume k is an integer and is greater than 0. Show all work.

Find in terms of for .

Use the graph to identify all discontinuities of f.

Determine all vertical and slant asymptotes.

For the function graphed below, identify or state that the limit does not exist.

Prove that the limit is correct using the appropriate definition. Show all work.

A ski rental shop charges $7.00 for each hour, or portion of an hour, its ski equipment is rented for up to a maximum of $56.00 for all day. If equals the total charge for the ski equipment for t hours, determine the limit , if it exists.

Use graphical and numerical evidence to determine if exists. If so, state the limit.

Sketch the graph of . What is ?

Preliminaries

Differentiation

Applications of the Derivative

Integration

Applications of the Definite Integral

Exponentials, Logarithms and Other Transcendental Functions

Integration Techniques

First-Order Differential Equations

Infinite Series

Parametric Equations and Polar Coordinates

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables and Partial Differentiation

Multiple Integrals

Vector Calculus

Second Order Differential Equations

Filters