Question 1

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

Accepted Answer

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

Question 2

Estimate the slope of   at   .

Accepted Answer

A)  -2.00 
B)  0.00 
C)  1.00 
D)  1.41 
A)  -2.00 
B)  0.00 
C)  1.00 
D)  1.41

Question 3

Determine where f is continuous.

Accepted Answer

A)  x ≠ 0 
B)  x > 0 
C)    
D)  continuous on all reals 
A)  x ≠ 0 
B)  x > 0 
C)    
D)  continuous on all reals

Question 4

Use graphical and numerical evidence to estimate the limit.

Accepted Answer

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

Question 5

Evaluate   where   .

Accepted Answer

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

Question 6

Determine the limit (answer as appropriate, with a number,     or does not exist).

Accepted Answer

A)  3 
B)    
C)    
D)    
E)  does not exist 
A)  3 
B)    
C)    
D)    
E)  does not exist

Question 7

Use the graph to identify all discontinuities of f.

Accepted Answer

The functi

Question 8

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 9

Estimate the slope of   at   .

Accepted Answer

A)  6 
B)  28 
C)  16 
D)  56 
A)  6 
B)  28 
C)  16 
D)  56

Question 10

Sketch the graph of   . What is   ?

Accepted Answer

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

Question 11

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 12

Evaluate the limit, if it exists.

Accepted Answer

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

Question 13

Find the limit or explain why it does not exist.

Accepted Answer

A)    
B)    
C)    
D)  The limit does not exist; the function is not defined for   . 
A)    
B)    
C)    
D)  The limit does not exist; the function is not defined for   .

Question 14

Determine the limit (answer as appropriate, with a number,     or does not exist).

Accepted Answer

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

Question 15

Find the limit or explain why it does not exist.

Accepted Answer

A)    
B)    
C)    
D)  The limit does not exist; the function is not defined for   . 
A)    
B)    
C)    
D)  The limit does not exist; the function is not defined for   .

Question 16

Suppose the length of an animal t days after birth is given by h(t).   mm What is the length of the animal at birth?

Accepted Answer

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

Question 17

Determine the limit (answer as appropriate, with a number,     or does not exist).

Accepted Answer

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

Question 18

Find   in terms of   for   .

Accepted Answer

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

Question 19

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

Accepted Answer

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

Question 20

Evaluate the limit, if it exists. Assume that

Accepted Answer

A)  0 
B)  10 
C)    
D)  The limit does not exist. 
A)  0 
B)  10 
C)    
D)  The limit does not exist.

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

Estimate the slope of at .

Determine where f is continuous.

Use graphical and numerical evidence to estimate the limit.

Evaluate where .

Determine the limit (answer as appropriate, with a number, or does not exist).

Use the graph to identify all discontinuities of f.

Find all discontinuities.

Estimate the slope of at .

Sketch the graph of . What is ?

Find all discontinuities.

Evaluate the limit, if it exists.

Find the limit or explain why it does not exist.

Determine the limit (answer as appropriate, with a number, or does not exist).

Find the limit or explain why it does not exist.

Suppose the length of an animal t days after birth is given by h(t). mm What is the length of the animal at birth?

Determine the limit (answer as appropriate, with a number, or does not exist).

Find in terms of for .

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

Evaluate the limit, if it exists. Assume that

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

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

Estimate the slope of at .

Determine where f is continuous.

Use graphical and numerical evidence to estimate the limit.

Evaluate where .

Determine the limit (answer as appropriate, with a number, or does not exist).

Use the graph to identify all discontinuities of f.

Find all discontinuities.

Estimate the slope of at .

Sketch the graph of . What is ?

Find all discontinuities.

Evaluate the limit, if it exists.

Find the limit or explain why it does not exist.

Determine the limit (answer as appropriate, with a number, or does not exist).

Find the limit or explain why it does not exist.

Suppose the length of an animal t days after birth is given by h(t). mm What is the length of the animal at birth?

Determine the limit (answer as appropriate, with a number, or does not exist).

Find in terms of for .

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

Evaluate the limit, if it exists. Assume that

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