Question 1

Find the limit or explain why it does not exist.

Accepted Answer

A)    
B)    
C)  The limit does not exist; the function increases without bound as x approaches 5 from the right. 
D)  The limit does not exist; the function is not defined for   . 
A)    
B)    
C)  The limit does not exist; the function increases without bound as x approaches 5 from the right. 
D)  The limit does not exist; the function is not defined for   .

Question 2

Given f(x), identify a specific   for which no   exists to satisfy the definition of a limit.   and   .

Accepted Answer

The answer of Given f(x), identify a specific  ...

Question 3

Evaluate the indicated limit, if it exists.

Accepted Answer

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

Question 4

Complete the table appropriately and use the numerical evidence to conjecture the value of   . x   -10
-100
-1000
-10,000

Accepted Answer

A)  8 
B)    
C)    
D)    
A)  8 
B)    
C)    
D)

Question 5

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

Accepted Answer

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

Question 6

Find N corresponding to   for   .

Accepted Answer

A)    
B)  50 
C)    
D)  -50 
A)    
B)  50 
C)    
D)  -50

Question 7

Suppose that a state's tax code states that tax liability is   % on the first   of taxable earnings and   % on the remainder. Find the constants a and b in the tax function T(x)   such that   and   exists.

Accepted Answer

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

Question 8

Sketch the graph of a function with the given properties.

Accepted Answer

One possible functio

Question 9

Determine the intervals where f is continuous.

Accepted Answer

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

Question 10

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

Accepted Answer

A)    
B)    
C)  5 
D)  The limit does not exist. 
A)    
B)    
C)  5 
D)  The limit does not exist.

Question 11

Evaluate the limit, if it exists.

Accepted Answer

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

Question 12

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

Accepted Answer

A)  0 
B)  2 
C)    
D)  does not exist 
A)  0 
B)  2 
C)    
D)  does not exist

Question 13

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

Accepted Answer

A)  4 
B)  -4 
C)  0 
D)  the limit does not exist 
A)  4 
B)  -4 
C)  0 
D)  the limit does not exist

Question 14

Find a   corresponding to M = 100 for   .

Accepted Answer

A)    
B)    
C)  0.0008 
D)    
A)    
B)    
C)  0.0008 
D)

Question 15

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 16

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

Accepted Answer

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

Question 17

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 18

Use the Intermediate Value Theorem to determine if f has a zero in the interval [1,7].

Accepted Answer

Since f(x) is continuous on the interval

Question 19

Estimate the slope of   at   .

Accepted Answer

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

Question 20

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

Find the limit or explain why it does not exist.

Given f(x), identify a specific for which no exists to satisfy the definition of a limit. and .

Evaluate the indicated limit, if it exists.

Complete the table appropriately and use the numerical evidence to conjecture the value of . x -10 -100 -1000 -10,000

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

Find N corresponding to for .

Suppose that a state's tax code states that tax liability is % on the first of taxable earnings and % on the remainder. Find the constants a and b in the tax function T(x) such that and exists.

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).

Evaluate the limit, if it exists.

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

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

Find a corresponding to M = 100 for .

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

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

Find all discontinuities.

Use the Intermediate Value Theorem to determine if f has a zero in the interval [1,7].

Estimate the slope of at .

Given that find the limit or explain why it 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

Find the limit or explain why it does not exist.

Given f(x), identify a specific for which no exists to satisfy the definition of a limit. and .

Evaluate the indicated limit, if it exists.

Complete the table appropriately and use the numerical evidence to conjecture the value of . x -10 -100 -1000 -10,000

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

Find N corresponding to for .

Suppose that a state's tax code states that tax liability is % on the first of taxable earnings and % on the remainder. Find the constants a and b in the tax function T(x) such that and exists.

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).

Evaluate the limit, if it exists.

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

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

Find a corresponding to M = 100 for .

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

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

Find all discontinuities.

Use the Intermediate Value Theorem to determine if f has a zero in the interval [1,7].

Estimate the slope of at .

Given that find the limit or explain why it 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