Question 1

Find the limit, if it exists.

Accepted Answer

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

Question 2

Let   and   .Find the rule for the function   .

Accepted Answer

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

Question 3

Determine whether the point (- 6, - 12) lies on the graph of the function

Accepted Answer

A) Yes, the point lies on the graph. 
B) No, the point does not lie on the graph. 
A) Yes, the point lies on the graph. 
B) No, the point does not lie on the graph.

Question 4

Evaluate h (3), where

Accepted Answer

A) 0.25 
B)    
C) 5.25 
D)    
E)    
A) 0.25 
B)    
C) 5.25 
D)    
E)

Question 5

A function f is continuous at the point   if the following conditions are satisfied.
1.   is defined.
2.   exists.
3.   .
Determine the value of x, if any, at which the function is discontinuous.       __________
State the condition(s) for continuity that are violated.
Conditions: __________

Accepted Answer

The answer of A function f is continuous at the...

Question 6

Let   . Find the average rate of change of y with respect to x in the interval from   to   , from   to   , from   to   , and the (instantaneous) rate of change of y at   .

Accepted Answer

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

Question 7

Find the domain of the function   Give the answer as an interval or union of intervals.

Accepted Answer

The answer of Find the domain of the function ...

Question 8

Find the one-sided limit, if it exists.If it does not, answer none.

Accepted Answer

The answer of Find the one-sided limit, if it exists.If...

Question 9

Find the domain of the function.

Accepted Answer

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

Question 10

Find the one-sided limit.

Accepted Answer

The answer of Find the one-sided limit.  ...

Question 11

The base salary of a salesman working on commission is $13,000.For each $50,000 of sales beyond $100,000 he is paid a $1,000 commission.Sketch a graph showing his earnings as a function of the level of his sales x.

Accepted Answer

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

Question 12

Complete the table by computing   at the given values of x.Use the results to guess at   if it exists.

Accepted Answer

A) x 1 5 10 100 1,000 f(x) 18 614 4,989 4,990,089 4,999,000,089
  
B) x 1 5 10 100 1,000 f(x) 18 614 4,439 4,989,539 4,998,999,539
  
C) x 1 5 10 100 1,000 f(x) 18 614 5,896 4,990,996 4,999,000,996
  
D) x 1 5 10 100 1,000 f(x) 18 614 4,914 4,990,014 4,999,000,014
  
A) x 1 5 10 100 1,000 f(x) 18 614 4,989 4,990,089 4,999,000,089
  
B) x 1 5 10 100 1,000 f(x) 18 614 4,439 4,989,539 4,998,999,539
  
C) x 1 5 10 100 1,000 f(x) 18 614 5,896 4,990,996 4,999,000,996
  
D) x 1 5 10 100 1,000 f(x) 18 614 4,914 4,990,014 4,999,000,014

Question 13

Use the graph of the function f to find   and   if the limit exists.

Accepted Answer

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

Question 14

Find the slope of the tangent line to the graph of each function at the given point and determine an equation of the tangent line.

Accepted Answer

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

Question 15

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

Accepted Answer

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

Question 16

Find the indicated one-sided limit.

Accepted Answer

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

Question 17

The number of cars running in the business district of a town at time t is given by f (t). Carbon monoxide pollution coming from these cars is given by g(x) parts per million, where x is the number of cars being operated in the district.What does the function   represent?

Accepted Answer

A) Carbon monoxide emission of the cars in the business district. 
B) Total number of cars emitting Carbon Monoxide in the business district town at given time t. 
C) Total number of cars in the business district town at given time t. 
D) Total number of Carbon Monoxide emitted in the business district town by the cars. 
E) Total Carbon monoxide emission of the cars in the business district town at given time t. 
A) Carbon monoxide emission of the cars in the business district. 
B) Total number of cars emitting Carbon Monoxide in the business district town at given time t. 
C) Total number of cars in the business district town at given time t. 
D) Total number of Carbon Monoxide emitted in the business district town by the cars. 
E) Total Carbon monoxide emission of the cars in the business district town at given time t.

Question 18

Let f be the function defined by

Accepted Answer

The answer of Let f be the function defined by
...

Question 19

Find the values of x for which the function is continuous.

Accepted Answer

The answer of Find the values of x for which...

Question 20

Find the limit, if it exists.

Accepted Answer

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

Find the limit, if it exists.

Let and .Find the rule for the function .

Determine whether the point (- 6, - 12) lies on the graph of the function

Evaluate h (3), where

A function f is continuous at the point if the following conditions are satisfied. 1. is defined. 2. exists. 3. . Determine the value of x, if any, at which the function is discontinuous. State the condition(s) for continuity that are violated. Conditions:

Let . Find the average rate of change of y with respect to x in the interval from to , from to , from to , and the (instantaneous) rate of change of y at .

Find the domain of the function Give the answer as an interval or union of intervals.

Find the one-sided limit, if it exists.If it does not, answer none.

Find the domain of the function.

Find the one-sided limit.

The base salary of a salesman working on commission is $13,000.For each $50,000 of sales beyond $100,000 he is paid a $1,000 commission.Sketch a graph showing his earnings as a function of the level of his sales x.

Complete the table by computing at the given values of x.Use the results to guess at if it exists.

Use the graph of the function f to find and if the limit exists.

Find the slope of the tangent line to the graph of each function at the given point and determine an equation of the tangent line.

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

Find the indicated one-sided limit.

The number of cars running in the business district of a town at time t is given by f (t). Carbon monoxide pollution coming from these cars is given by g(x) parts per million, where x is the number of cars being operated in the district.What does the function represent?

Let f be the function defined by

Find the values of x for which the function is continuous.

Find the limit, if it exists.

Preliminaries

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Integration

Additional Topics in Integration

Calculus of Several Variables

Filters

Exam 2: Functions, Limits and the Derivative

Find the limit, if it exists.

Let and .Find the rule for the function .

Determine whether the point (- 6, - 12) lies on the graph of the function

Evaluate h (3), where

A function f is continuous at the point if the following conditions are satisfied. 1. is defined. 2. exists. 3. . Determine the value of x, if any, at which the function is discontinuous. __________ State the condition(s) for continuity that are violated. Conditions: __________

Let . Find the average rate of change of y with respect to x in the interval from to , from to , from to , and the (instantaneous) rate of change of y at .

Find the domain of the function Give the answer as an interval or union of intervals.

Find the one-sided limit, if it exists.If it does not, answer none.

Find the domain of the function.

Find the one-sided limit.

The base salary of a salesman working on commission is $13,000.For each $50,000 of sales beyond $100,000 he is paid a $1,000 commission.Sketch a graph showing his earnings as a function of the level of his sales x.

Complete the table by computing at the given values of x.Use the results to guess at if it exists.

Use the graph of the function f to find and if the limit exists.

Find the slope of the tangent line to the graph of each function at the given point and determine an equation of the tangent line.

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

Find the indicated one-sided limit.

The number of cars running in the business district of a town at time t is given by f (t). Carbon monoxide pollution coming from these cars is given by g(x) parts per million, where x is the number of cars being operated in the district.What does the function represent?

Let f be the function defined by

Find the values of x for which the function is continuous.

Find the limit, if it exists.

Preliminaries

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Integration

Additional Topics in Integration

Calculus of Several Variables

Filters

A function f is continuous at the point if the following conditions are satisfied. 1. is defined. 2. exists. 3. . Determine the value of x, if any, at which the function is discontinuous. State the condition(s) for continuity that are violated. Conditions: