Question 1

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 D

Question 2

Determine the intervals where f is continuous.

Accepted Answer

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

Question 3

Estimate the slope of   at   .

Accepted Answer

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

Question 4

Given   and   , find   .

Accepted Answer

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

Question 5

Determine the values of a and b that make f(x) continuous.   Use   .

Accepted Answer

A)    
B)    
C)    
D)  No values of a and b will make f(x) continuous. 
A)    
B)    
C)    
D)  No values of a and b will make f(x) continuous.

Question 6

Sketch the graph of a function with the given properties.

Accepted Answer

One possible functio

Question 7

Determine the intervals where f is continuous.

Accepted Answer

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

Question 8

Find the limit exactly (Hint: multiply and divide by the conjugate expression and simplify).

Accepted Answer

A)  -4 
B)  0 
C)  6 
D)    
A)  -4 
B)  0 
C)  6 
D)

Question 9

Find all horizontal and vertical asymptotes of f(x).   For each vertical asymptote, determine whether   or   on either side of the vertical asymptote.

Accepted Answer

A)  horizontal asymptote   ; there are no vertical asymptotes. 
B)  horizontal asymptote at   , vertical asymptotes at   ;         
C)  horizontal asymptote at   , vertical asymptotes at   ;         
D)  horizontal asymptote at   , vertical asymptotes at   ;         
A)  horizontal asymptote   ; there are no vertical asymptotes. 
B)  horizontal asymptote at   , vertical asymptotes at   ;         
C)  horizontal asymptote at   , vertical asymptotes at   ;         
D)  horizontal asymptote at   , vertical asymptotes at   ;

Question 10

Find a   corresponding to M = 100 for   .

Accepted Answer

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

Question 11

Complete the tables appropriately and use the numerical evidence to conjecture the value of   . x   1.9
1)99
1)999
1)9999
X   2.1
2)01
2)001
2)0001

Accepted Answer

A)  0 
B)  5 
C)  -10 
D)  2 
A)  0 
B)  5 
C)  -10 
D)  2

Question 12

Find all discontinuities.   For each discontinuity that is removable, define a new function that removes the discontinuity.

Accepted Answer

discontinuous at @#IMG-DLM& Th

Question 13

Determine all vertical and slant asymptotes.

Accepted Answer

A)  vertical asymptotes:     slant asymptote:   
B)  vertical asymptotes:     slant asymptote:   
C)  vertical asymptote:   slant asymptote:   
D)  vertical asymptote: none; slant asymptote:   
A)  vertical asymptotes:     slant asymptote:   
B)  vertical asymptotes:     slant asymptote:   
C)  vertical asymptote:   slant asymptote:   
D)  vertical asymptote: none; slant asymptote:

Question 14

Consider   .
a. Use a graph and numerical values of the function to conjecture a value of   .   b. Rewrite the function to avoid loss-of-significance error.

Accepted Answer

a. Graphs should show significant oscill

Question 15

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

Accepted Answer

A)    
B)    
C)  25 
D)  The limit does not exist. 
A)    
B)    
C)  25 
D)  The limit does not exist.

Question 16

Suppose that the size of the pupil of a certain animal is given by   (mm), where x is the intensity of the light on the pupil. If   find the size of the pupil with no light and the size of the pupil with an infinite amount of light.

Accepted Answer

A)  no light:   mm; infinite light:   mm 
B)  no light:   mm; infinite light:   mm 
C)  no light:   mm; infinite light: 0 mm 
D)  no light:   mm; infinite light:   mm 
A)  no light:   mm; infinite light:   mm 
B)  no light:   mm; infinite light:   mm 
C)  no light:   mm; infinite light: 0 mm 
D)  no light:   mm; infinite light:   mm

Question 17

Evaluate the limit, if it exists. Assume that

Accepted Answer

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

Question 18

Evaluate the limit, if it exists.

Accepted Answer

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

Question 19

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

Accepted Answer

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

Question 20

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

Accepted Answer

A)  0 
B)  1 
C)  3 
D)  does not exist 
A)  0 
B)  1 
C)  3 
D)  does not exist

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

Determine the intervals where f is continuous.

Estimate the slope of at .

Given and , find .

Determine the values of a and b that make f(x) continuous. Use .

Sketch the graph of a function with the given properties.

Determine the intervals where f is continuous.

Find the limit exactly (Hint: multiply and divide by the conjugate expression and simplify).

Find all horizontal and vertical asymptotes of f(x). For each vertical asymptote, determine whether or on either side of the vertical asymptote.

Find a corresponding to M = 100 for .

Complete the tables appropriately and use the numerical evidence to conjecture the value of . x 1.9 1)99 1)999 1)9999 X 2.1 2)01 2)001 2)0001

Find all discontinuities. For each discontinuity that is removable, define a new function that removes the discontinuity.

Determine all vertical and slant asymptotes.

Consider . a. Use a graph and numerical values of the function to conjecture a value of . b. Rewrite the function to avoid loss-of-significance error.

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

Suppose that the size of the pupil of a certain animal is given by (mm), where x is the intensity of the light on the pupil. If find the size of the pupil with no light and the size of the pupil with an infinite amount of light.

Evaluate the limit, if it exists. Assume that

Evaluate the limit, if it exists.

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

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

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

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

Determine the intervals where f is continuous.

Estimate the slope of at .

Given and , find .

Determine the values of a and b that make f(x) continuous. Use .

Sketch the graph of a function with the given properties.

Determine the intervals where f is continuous.

Find the limit exactly (Hint: multiply and divide by the conjugate expression and simplify).

Find all horizontal and vertical asymptotes of f(x). For each vertical asymptote, determine whether or on either side of the vertical asymptote.

Find a corresponding to M = 100 for .

Complete the tables appropriately and use the numerical evidence to conjecture the value of . x 1.9 1)99 1)999 1)9999 X 2.1 2)01 2)001 2)0001

Find all discontinuities. For each discontinuity that is removable, define a new function that removes the discontinuity.

Determine all vertical and slant asymptotes.

Consider . a. Use a graph and numerical values of the function to conjecture a value of . b. Rewrite the function to avoid loss-of-significance error.

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

Suppose that the size of the pupil of a certain animal is given by (mm), where x is the intensity of the light on the pupil. If find the size of the pupil with no light and the size of the pupil with an infinite amount of light.

Evaluate the limit, if it exists. Assume that

Evaluate the limit, if it exists.

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

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

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