Question 1

Find the point on the graph of   that is closest to the point   .

Accepted Answer

The answer of Find the point on the graph of...

Question 2

Each of the following functions restricted to the given interval attains a minimum and maximum value. Which attain their maximum or minimum value at a point in the interior of the interval?
A)   on   
B)   on   
C)   on   
D)   on

Accepted Answer

The answer of Each of the following functions restricted to...

Question 3

Find a point   satisfying the conclusion of the Mean Value Theorem for the function   in the interval   .

Accepted Answer

The answer of Find a point   satisfying the...

Question 4

Let   . 
A) Show that there is no   such that   . 
B) Explain why the above does not contradict the MVT.

Accepted Answer

B) @#IMG-DLM& is not

Question 5

For the function   , find the transition points, intervals of increase/decrease, concavity, and asymptotic behavior. Then sketch the graph using this information.

Accepted Answer

Nnmm
Intervals of increase: @#IMG-DLM& I

Question 6

Sketch the graph of the function   .
Indicate the asymptotes, local extrema, and points of inflection if they exist.

Accepted Answer

Asymptote: @#IMG-DLM& Local ex

Question 7

The tangent line to   at a point   intersects the   and   axes at points   and   , respectively. Find   such that the area of the triangle   is maximum.

Accepted Answer

The answer of The tangent line to   at...

Question 8

Estimate the roots of the equation   using the linear approximation for   at   .

Accepted Answer

The answer of Estimate the roots of the equation ...

Question 9

Find the angles of the isosceles triangle of minimum area in which a circle of radius   is inscribed.
What are the sides of this triangle?
(You don't have to prove that the area is a minimum.)

Accepted Answer

The angles are each

Question 10

Find the linearization of the given function centered at   and use it to estimate   . 
A)   
B)

Accepted Answer

The answer of Find the linearization of the given function...

Question 11

A manufacturer sells instruments for   per unit.
The cost of producing   instruments is   , and no more than   instruments can be produced in a week.
Find the amount of instruments that should be produced in a week to obtain maximum profit.

Accepted Answer

The answer of A manufacturer sells instruments for  ...

Question 12

Let   be the function on   given by   and the graph:   The MVT can be applied on the following interval:

Accepted Answer

A)    
B)    
C)    
D)    
E)  A and C are correct. 
A)    
B)    
C)    
D)    
E)  A and C are correct.

Question 13

Which of the following functions does not have horizontal asymptotes?

Accepted Answer

A)    
B)    
C)    
D)    
E)  None of the above. 
A)    
B)    
C)    
D)    
E)  None of the above.

Question 14

Given   ,
Which of the following statements is correct?

Accepted Answer

A)    is increasing on   and decreasing on   . 
B)    is increasing on   . 
C)    is decreasing on   . 
D)    is decreasing on   and increasing on   . 
E)    is decreasing on   and increasing on   . 
A)    is increasing on   and decreasing on   . 
B)    is increasing on   . 
C)    is decreasing on   . 
D)    is decreasing on   and increasing on   . 
E)    is decreasing on   and increasing on   .

Question 15

Sketch the graph of a function such that   for     for     for     for

Accepted Answer

The answer of Sketch the graph of a function such...

Question 16

Find all the critical points of the following functions (if they exist)
A)   
B)   
C)

Accepted Answer

The answer of Find all the critical points of the...

Question 17

Estimate the value of   using the linear approximation and find the error using a calculator.

Accepted Answer

The answer of Estimate the value of   using...

Question 18

A farmer wants to fence in a rectangular field for livestock. The boundary for one
side of the field is a long, straight river. No fencing is needed on this side. For the
remaining three sides, he has 400 meters of fencing available. What are the dimensions of the largest rectangular area that can be formed with this amount of fencing?

Accepted Answer

Width: 100 meters
Length: 200

Question 19

Show that the equation   has a solution in the interval   and use Newton's Method to approximate it within an error of at most   .

Accepted Answer

The answer of Show that the equation   has...

Question 20

Use Newton's Method with   to find an approximate root for   and use it to approximate   to within an error of at most   .

Accepted Answer

The answer of Use Newton's Method with   to...

Find the point on the graph of that is closest to the point .

Each of the following functions restricted to the given interval attains a minimum and maximum value. Which attain their maximum or minimum value at a point in the interior of the interval? A) on B) on C) on D) on

Find a point satisfying the conclusion of the Mean Value Theorem for the function in the interval .

Let . A) Show that there is no such that . B) Explain why the above does not contradict the MVT.

For the function , find the transition points, intervals of increase/decrease, concavity, and asymptotic behavior. Then sketch the graph using this information.

Sketch the graph of the function . Indicate the asymptotes, local extrema, and points of inflection if they exist.

The tangent line to at a point intersects the and axes at points and , respectively. Find such that the area of the triangle is maximum.

Estimate the roots of the equation using the linear approximation for at .

Find the angles of the isosceles triangle of minimum area in which a circle of radius is inscribed. What are the sides of this triangle? (You don't have to prove that the area is a minimum.)

Find the linearization of the given function centered at and use it to estimate . A) B)

A manufacturer sells instruments for per unit. The cost of producing instruments is , and no more than instruments can be produced in a week. Find the amount of instruments that should be produced in a week to obtain maximum profit.

Let be the function on given by and the graph: The MVT can be applied on the following interval:

Which of the following functions does not have horizontal asymptotes?

Given , Which of the following statements is correct?

Sketch the graph of a function such that for for for for

Find all the critical points of the following functions (if they exist) A) B) C)

Estimate the value of using the linear approximation and find the error using a calculator.

Show that the equation has a solution in the interval and use Newton's Method to approximate it within an error of at most .

Use Newton's Method with to find an approximate root for and use it to approximate to within an error of at most .

Precalculus Review

Limits

Differentiation

The Integral

Applications of the Integral

Exponential Functions

Techniques of Integration

Further Applications of the Integral and Taylor Polynomials

Introduction to Differential Equations

Infinite Series

Parametric Equations, Polar Coordinates, and Conic Sections

Vector Geometry

Calculus of Vector-Valued Functions

Differentiation in Several Variables

Multiple Integration

Line and Surface Integrals

Fundamental Theorems of Vector Analysis

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Exam 4: Applications of the Derivative

Find the point on the graph of that is closest to the point .

Each of the following functions restricted to the given interval attains a minimum and maximum value. Which attain their maximum or minimum value at a point in the interior of the interval? A) on B) on C) on D) on

Find a point satisfying the conclusion of the Mean Value Theorem for the function in the interval .

Let . A) Show that there is no such that . B) Explain why the above does not contradict the MVT.

For the function , find the transition points, intervals of increase/decrease, concavity, and asymptotic behavior. Then sketch the graph using this information.

Sketch the graph of the function . Indicate the asymptotes, local extrema, and points of inflection if they exist.

The tangent line to at a point intersects the and axes at points and , respectively. Find such that the area of the triangle is maximum.

Estimate the roots of the equation using the linear approximation for at .

Find the angles of the isosceles triangle of minimum area in which a circle of radius is inscribed. What are the sides of this triangle? (You don't have to prove that the area is a minimum.)

Find the linearization of the given function centered at and use it to estimate . A) B)

A manufacturer sells instruments for per unit. The cost of producing instruments is , and no more than instruments can be produced in a week. Find the amount of instruments that should be produced in a week to obtain maximum profit.

Let be the function on given by and the graph: The MVT can be applied on the following interval:

Which of the following functions does not have horizontal asymptotes?

Given , Which of the following statements is correct?

Sketch the graph of a function such that for for for for

Find all the critical points of the following functions (if they exist) A) B) C)

Estimate the value of using the linear approximation and find the error using a calculator.

Show that the equation has a solution in the interval and use Newton's Method to approximate it within an error of at most .

Use Newton's Method with to find an approximate root for and use it to approximate to within an error of at most .

Precalculus Review

Limits

Differentiation

The Integral

Applications of the Integral

Exponential Functions

Techniques of Integration

Further Applications of the Integral and Taylor Polynomials

Introduction to Differential Equations

Infinite Series

Parametric Equations, Polar Coordinates, and Conic Sections

Vector Geometry

Calculus of Vector-Valued Functions

Differentiation in Several Variables

Multiple Integration

Line and Surface Integrals

Fundamental Theorems of Vector Analysis

Filters