Question 1

Using a calculator or computer, estimate the absolute extrema of   on the interval   . Round answer to the nearest hundredth.

Accepted Answer

A)  absolute max:   ; absolute min:   
B)  absolute max:   ; absolute min:   
C)  absolute max:   ; absolute min:   
D)  absolute max:   ; absolute min:   
A)  absolute max:   ; absolute min:   
B)  absolute max:   ; absolute min:   
C)  absolute max:   ; absolute min:   
D)  absolute max:   ; absolute min:

Question 2

$\omega$
-The impedance Z of a simple RL (resistive inductive) circuit is given by   , where R is the resistance of the resistor, L is the inductance of the inductor, and $\omega$ is the angular frequency of the applied voltage. Find a linear approximation of Z(L) for small values of L assuming all other quantities are constant. Show all of your work.

Accepted Answer

The answer of $\omega$
-The impedance Z of a simple RL...

Question 3

The unit price of x units of a certain product is given by   . What is the maximum possible revenue when selling x units? Round answer to nearest dollar.

Accepted Answer

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

Question 4

Estimate critical numbers and sketch graphs showing both global and local behavior.

Accepted Answer

critical numbers: @#IMG-DLM& @#IMG-DLM&

Question 5

Find all critical numbers of   and use the First Derivative Test to classify each as a local minimum, local maximum or neither.

Accepted Answer

A)  local maximum: none local minimum: none
Neither at   
B)  local maximum at   local minimum at  
Neither at   
C)  local maximum at   local minimum at  
Neither at   
D)  local maximum: none local minimum at  
Neither at   and   
A)  local maximum: none local minimum: none
Neither at   
B)  local maximum at   local minimum at  
Neither at   
C)  local maximum at   local minimum at  
Neither at   
D)  local maximum: none local minimum at  
Neither at   and

Question 6

Bubba, a farmer, wants to build a pen using the 20 ft   40 ft corner of his barn as part of the pen as shown in the figure below (the corner will not require any fencing). If Bubba has 124 ft of available fencing, then what will be the maximum area?

Accepted Answer

A)  2116 square feet 
B)  1681 square feet 
C)  1296 square feet 
D)  961 square feet 
A)  2116 square feet 
B)  1681 square feet 
C)  1296 square feet 
D)  961 square feet

Question 7

Determine the equation of the slant asymptote of   .

Accepted Answer

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

Question 8

Use a linear approximation to estimate

Accepted Answer

A)  0 
B)  0.18 
C)  0.1 
D)  0.02 
A)  0 
B)  0.18 
C)  0.1 
D)  0.02

Question 9

A Norman window has the outline of a semicircle on top of a rectangle. Suppose there is   feet of wood trim available. Find the dimensions of the rectangle (and, hence, the semicircle) that will maximize the area of the window.

Accepted Answer

A)  base:   ft; height:   ft 
B)  base:   ft; height:   ft 
C)  base:   ft; height:   ft 
D)  base:   ft; height:   ft 
A)  base:   ft; height:   ft 
B)  base:   ft; height:   ft 
C)  base:   ft; height:   ft 
D)  base:   ft; height:   ft

Question 10

Using Newton's method with   , determine the third iteration when approximating the root to at least six-digit accuracy of the following equation. x3 + x2 - 5x + 4 = 0

Accepted Answer

A)  -3.062500 
B)  -3.060647 
C)  -3.060691 
D)  -3.060992 
A)  -3.062500 
B)  -3.060647 
C)  -3.060691 
D)  -3.060992

Question 11

Find the linear approximation at x = 0 to show that the following commonly used approximation is valid for "small" x.

Accepted Answer

The answer of Find the linear approximation at x =...

Question 12

Determine all significant features and sketch a graph.

Accepted Answer

domain: @#IMG-DLM& range: @#IMG-DLM& x-intercept:

Question 13

Explain why Newton's method fails for the following equation with the specified initial guess.

Accepted Answer

A)  Using   we see that f is not differentiable at   
B)  Using   we obtain   . 
C)  Using   we obtain   which will give   
D)  Using   we see that f does not have any real roots. 
A)  Using   we see that f is not differentiable at   
B)  Using   we obtain   . 
C)  Using   we obtain   which will give   
D)  Using   we see that f does not have any real roots.

Question 14

Find the x-coordinates of all extrema and sketch the graph showing global and local behavior of the function. Round answers to nearest thousandth. y = x5 - 150x3 + 460x + 9

Accepted Answer

A)  local max: x = -1.017, x = 9.432 local min: x = -9.432, x = 1.017   
B)  local max: x = -9.432, x = 1.017 local min: x = -1.017, x = 9.432   
C)  local max: x = -1.0343 local min: x = 1.0343   
D)  local max: x = 1.0343 local min: x = -1.0343   
A)  local max: x = -1.017, x = 9.432 local min: x = -9.432, x = 1.017   
B)  local max: x = -9.432, x = 1.017 local min: x = -1.017, x = 9.432   
C)  local max: x = -1.0343 local min: x = 1.0343   
D)  local max: x = 1.0343 local min: x = -1.0343

Question 15

Using the critical numbers of   , use the Second Derivative Test to determine all local extrema.

Accepted Answer

@#IMG-DLM& ; @#IMG-DLM& and @#IMG-DLM& is a local

Question 16

Estimate the intervals where the function shown below is concave up and/or concave down.

Accepted Answer

A)  concave up for   concave down for   
B)  concave up for   concave down for   
C)  concave up for   concave down for   
D)  concave up for   concave down for   
A)  concave up for   concave down for   
B)  concave up for   concave down for   
C)  concave up for   concave down for   
D)  concave up for   concave down for

Question 17

Use a linear approximation to estimate   Note that 17.2 is near 16 which is

Accepted Answer

A)  3.23649 
B)  2.03649 
C)  2.0375 
D)  3.08312 
A)  3.23649 
B)  2.03649 
C)  2.0375 
D)  3.08312

Question 18

Determine, by hand, the interval(s) where   is increasing and/or decreasing.

Accepted Answer

A)  increasing   and   ; decreasing   
B)  increasing   ; decreasing   
C)  increasing   and   ; decreasing   and   
D)  increasing   ; decreasing   and   
A)  increasing   and   ; decreasing   
B)  increasing   ; decreasing   
C)  increasing   and   ; decreasing   and   
D)  increasing   ; decreasing   and

Question 19

Using a calculator or computer, estimate the absolute extrema of   , on the interval   .

Accepted Answer

A)  absolute max:   ; absolute min:   
B)  absolute max:   ; absolute min:   
C)  absolute max:   ; absolute min:   
D)  absolute max:   ; absolute min:   
A)  absolute max:   ; absolute min:   
B)  absolute max:   ; absolute min:   
C)  absolute max:   ; absolute min:   
D)  absolute max:   ; absolute min:

Question 20

Given   determine the critical number(s).

Accepted Answer

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

Using a calculator or computer, estimate the absolute extrema of on the interval . Round answer to the nearest hundredth.

The unit price of x units of a certain product is given by . What is the maximum possible revenue when selling x units? Round answer to nearest dollar.

Estimate critical numbers and sketch graphs showing both global and local behavior.

Find all critical numbers of and use the First Derivative Test to classify each as a local minimum, local maximum or neither.

Bubba, a farmer, wants to build a pen using the 20 ft 40 ft corner of his barn as part of the pen as shown in the figure below (the corner will not require any fencing). If Bubba has 124 ft of available fencing, then what will be the maximum area?

Determine the equation of the slant asymptote of .

Use a linear approximation to estimate

A Norman window has the outline of a semicircle on top of a rectangle. Suppose there is feet of wood trim available. Find the dimensions of the rectangle (and, hence, the semicircle) that will maximize the area of the window.

Using Newton's method with , determine the third iteration when approximating the root to at least six-digit accuracy of the following equation. x³ + x² - 5x + 4 = 0

Find the linear approximation at x = 0 to show that the following commonly used approximation is valid for "small" x.

Determine all significant features and sketch a graph.

Explain why Newton's method fails for the following equation with the specified initial guess.

Find the x-coordinates of all extrema and sketch the graph showing global and local behavior of the function. Round answers to nearest thousandth. y = x⁵ - 150x³ + 460x + 9

Using the critical numbers of , use the Second Derivative Test to determine all local extrema.

Estimate the intervals where the function shown below is concave up and/or concave down.

Use a linear approximation to estimate Note that 17.2 is near 16 which is

Determine, by hand, the interval(s) where is increasing and/or decreasing.

Using a calculator or computer, estimate the absolute extrema of , on the interval .

Given determine the critical number(s).

Preliminaries

Limits and Continuity

Differentiation

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 4: Applications of the Derivative

Using a calculator or computer, estimate the absolute extrema of on the interval . Round answer to the nearest hundredth.

The unit price of x units of a certain product is given by . What is the maximum possible revenue when selling x units? Round answer to nearest dollar.

Estimate critical numbers and sketch graphs showing both global and local behavior.

Find all critical numbers of and use the First Derivative Test to classify each as a local minimum, local maximum or neither.

Bubba, a farmer, wants to build a pen using the 20 ft 40 ft corner of his barn as part of the pen as shown in the figure below (the corner will not require any fencing). If Bubba has 124 ft of available fencing, then what will be the maximum area?

Determine the equation of the slant asymptote of .

Use a linear approximation to estimate

A Norman window has the outline of a semicircle on top of a rectangle. Suppose there is feet of wood trim available. Find the dimensions of the rectangle (and, hence, the semicircle) that will maximize the area of the window.

Using Newton's method with , determine the third iteration when approximating the root to at least six-digit accuracy of the following equation. x3 + x2 - 5x + 4 = 0

Find the linear approximation at x = 0 to show that the following commonly used approximation is valid for "small" x.

Determine all significant features and sketch a graph.

Explain why Newton's method fails for the following equation with the specified initial guess.

Find the x-coordinates of all extrema and sketch the graph showing global and local behavior of the function. Round answers to nearest thousandth. y = x5 - 150x3 + 460x + 9

Using the critical numbers of , use the Second Derivative Test to determine all local extrema.

Estimate the intervals where the function shown below is concave up and/or concave down.

Use a linear approximation to estimate Note that 17.2 is near 16 which is

Determine, by hand, the interval(s) where is increasing and/or decreasing.

Using a calculator or computer, estimate the absolute extrema of , on the interval .

Given determine the critical number(s).

Preliminaries

Limits and Continuity

Differentiation

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

Using Newton's method with , determine the third iteration when approximating the root to at least six-digit accuracy of the following equation. x³ + x² - 5x + 4 = 0

Find the x-coordinates of all extrema and sketch the graph showing global and local behavior of the function. Round answers to nearest thousandth. y = x⁵ - 150x³ + 460x + 9