Question 1

The solution of   + 2x - 15 ≥ 0 is

Accepted Answer

A)  x ≤ -5. 
B)  x ≥ -5. 
C)  x ≥ 3. 
D)  -5 ≤ x ≤ 3. 
E)  x ≤ -5, x ≥ 3. 
A)  x ≤ -5. 
B)  x ≥ -5. 
C)  x ≥ 3. 
D)  -5 ≤ x ≤ 3. 
E)  x ≤ -5, x ≥ 3.

Question 2

Let f(x)=   
.For each of the following,find the limit.If the limit does not exist,so state or use the symbol ∞ or -∞ where appropriate.Hint: Sketch the graph of f.
(a)   
f(x)
(b)   
f(x)
(c)   
f(x)
(d)   
f(x)
(e)   
f(x)

Accepted Answer

(a)5
(b)4

Question 3

The greatest integer function in mathematics (denoted f(x)=   
)is used every day by cashiers making change for customers.This function tells the amount of paper money for each amount of change owed.(For example,if the customer is owed $1.25 in change,he would get $1 in paper money,thus   
= 1).By considering   
,   
,   
,   
,and   
,determine   
   
.

Accepted Answer

The limit does not e

Question 4

The solution of   > 0 is

Accepted Answer

A)  1  3. 
B)  -1  3. 
E)  x  3. 
A)  1  3. 
B)  -1  3. 
E)  x  3.

Question 5

The length of a material increases as it is heated up according to the equation   
The rate at which the length is increasing is given by:   
Calculate this limit.

Accepted Answer

The answer of The length of a material increases as...

Question 6

The volume of helium in a spherical balloon (in cubic centimeters)as a function of the radius,r,in centimeters,is given by V(r)=   
π   
.Find   
V(r).

Accepted Answer

The answer of The volume of helium in a spherical...

Question 7

Find:

Accepted Answer

The answer of Find:   
  ...

Question 8

Find:   
   
.If the limit does not exist,so state or use the symbol ∞ or -∞ if appropriate.

Accepted Answer

The answer of Find:   
   
.If...

Question 9

The revenue function for a certain product is given by R(x)= 500x -   
.Graph this function in the window   
×   
.Use TRACE to estimate   
R(x).

Accepted Answer

The answer of The revenue function for a certain product...

Question 10

Find:

Accepted Answer

The answer of Find:   
  ...

Question 11

=

Accepted Answer

A)  0 
B)    
C)    
D)  -∞ 
E)  ∞ 
A)  0 
B)    
C)    
D)  -∞ 
E)  ∞

Question 12

The yearly sales y of a certain company (in thousands of dollars)is related to the amount that company spends on advertising,x (in thousands of dollars),according to the equation y(x)=   
.Graph this function on your graphing calculator in the window   
×   
.Use TRACE to explore   
y(x)and discuss what this means to the company.

Accepted Answer

@#IMG-DLM&_TB6578_11 y(x)= 1000.The grea

Question 13

If f(x)=   ,then  
F(x)=

Accepted Answer

A)  0 
B)  2 
C)  -∞ 
D)  ∞ 
E)  does not exist 
A)  0 
B)  2 
C)  -∞ 
D)  ∞ 
E)  does not exist

Question 14

Find the value(s)of x for which f(x)=   
is discontinuous.

Accepted Answer

The answer of Find the value(s)of x for which f(x)=...

Question 15

A math tutor charges $30 for the first hour of work at your house and $20 for every hour (or fraction thereof)afterwards.The function for what the session will cost you is given by:
f(x)=   
(a)Find   
f(x)
(b)Find   
f(x)
(c)Find   
f(x)

Accepted Answer

(a)the limit does not exist
(b

Question 16

The demand function for a certain product is given by: p =   
,where p is the price and q is the quantity demanded.
(a)Find the values of q for which p > 0.
(b)Find the values of q for which p < 0.
(c)What do the results of (a)and (b)mean and why does this make sense?

Accepted Answer

(a)p > 0 for all values of q
(

Question 17

(2 +  
)=

Accepted Answer

A)  0 
B)    
C)  -2 +   
D)  2 +   
E)  does not exist 
A)  0 
B)    
C)  -2 +   
D)  2 +   
E)  does not exist

Question 18

The yearly sales y of a certain company (in thousands of dollars)is related to the amount that company spends on advertising,x (in thousands of dollars),according to the equation y(x)=   
.Find   
y(x)and discuss what this means to the company.

Accepted Answer

@#IMG-DLM&_TB6578_11 y(x)= 1000.The grea

Question 19

The cost C of processing exhaust gases so that you remove all but x percent of the pollutants is given by   
Find the values of x for which C < 0.Discuss the meaning of the results.

Accepted Answer

C < 0 for x > 100 or x < 0.Nei

Question 20

Find the value(s)of x for which f(x)= 10 is discontinuous.

Accepted Answer

The answer of Find the value(s)of x for which f(x)=...

The solution of + 2x - 15 ≥ 0 is

Let f(x)= .For each of the following,find the limit.If the limit does not exist,so state or use the symbol ∞ or -∞ where appropriate.Hint: Sketch the graph of f. (a) f(x) (b) f(x) (c) f(x) (d) f(x) (e) f(x)

The solution of > 0 is

The length of a material increases as it is heated up according to the equation The rate at which the length is increasing is given by: Calculate this limit.

The volume of helium in a spherical balloon (in cubic centimeters)as a function of the radius,r,in centimeters,is given by V(r)= π .Find V(r).

Find:

Find: .If the limit does not exist,so state or use the symbol ∞ or -∞ if appropriate.

The revenue function for a certain product is given by R(x)= 500x - .Graph this function in the window × .Use TRACE to estimate R(x).

Find:

=

If f(x)= ,then F(x)=

Find the value(s)of x for which f(x)= is discontinuous.

The demand function for a certain product is given by: p = ,where p is the price and q is the quantity demanded. (a)Find the values of q for which p > 0. (b)Find the values of q for which p < 0. (c)What do the results of (a)and (b)mean and why does this make sense?

(2 + )=

The yearly sales y of a certain company (in thousands of dollars)is related to the amount that company spends on advertising,x (in thousands of dollars),according to the equation y(x)= .Find y(x)and discuss what this means to the company.

The cost C of processing exhaust gases so that you remove all but x percent of the pollutants is given by Find the values of x for which C < 0.Discuss the meaning of the results.

Find the value(s)of x for which f(x)= 10 is discontinuous.

Review of Algebra

Applications and More Algebra

Functions and Graphs

Lines parabolas and Systems

Exponential and Logarithmic Functions

Mathematics of Finance

Matrix Algebra

Linear Programming

Introduction to Probability and Statistics

Additional Topics in Probability

Differentiation

Additional Differentiation Topics

Curve Sketching

Integration

Methods and Applications of Integration

Continuous Random Variables

Multivariable Calculus

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Exam 11: Limits and Continuity

The solution of + 2x - 15 ≥ 0 is

Let f(x)= .For each of the following,find the limit.If the limit does not exist,so state or use the symbol ∞ or -∞ where appropriate.Hint: Sketch the graph of f. (a) f(x) (b) f(x) (c) f(x) (d) f(x) (e) f(x)

The solution of > 0 is

The length of a material increases as it is heated up according to the equation The rate at which the length is increasing is given by: Calculate this limit.

The volume of helium in a spherical balloon (in cubic centimeters)as a function of the radius,r,in centimeters,is given by V(r)= π .Find V(r).

Find:

Find: .If the limit does not exist,so state or use the symbol ∞ or -∞ if appropriate.

The revenue function for a certain product is given by R(x)= 500x - .Graph this function in the window × .Use TRACE to estimate R(x).

Find:

=

If f(x)= ,then F(x)=

Find the value(s)of x for which f(x)= is discontinuous.

A math tutor charges $30 for the first hour of work at your house and $20 for every hour (or fraction thereof)afterwards.The function for what the session will cost you is given by: f(x)= (a)Find f(x) (b)Find f(x) (c)Find f(x)

The demand function for a certain product is given by: p = ,where p is the price and q is the quantity demanded. (a)Find the values of q for which p > 0. (b)Find the values of q for which p < 0. (c)What do the results of (a)and (b)mean and why does this make sense?

(2 + )=

The yearly sales y of a certain company (in thousands of dollars)is related to the amount that company spends on advertising,x (in thousands of dollars),according to the equation y(x)= .Find y(x)and discuss what this means to the company.

The cost C of processing exhaust gases so that you remove all but x percent of the pollutants is given by Find the values of x for which C < 0.Discuss the meaning of the results.

Find the value(s)of x for which f(x)= 10 is discontinuous.

Review of Algebra

Applications and More Algebra

Functions and Graphs

Lines parabolas and Systems

Exponential and Logarithmic Functions

Mathematics of Finance

Matrix Algebra

Linear Programming

Introduction to Probability and Statistics

Additional Topics in Probability

Differentiation

Additional Differentiation Topics

Curve Sketching

Integration

Methods and Applications of Integration

Continuous Random Variables

Multivariable Calculus

Filters