Question 1

Use Newton's Method to find the solution of the equation x + tan x = 0 on the interval [2, 3] accurate to four decimal places.

Accepted Answer

A)  2.0288 
B)  2.0293 
C)  2.0278 
D)  2.0272 
E)  2.0284 
A)  2.0288 
B)  2.0293 
C)  2.0278 
D)  2.0272 
E)  2.0284

Question 2

Find the extreme values of f(x) = x +   cos x on [0, π].

Accepted Answer

The absolute maximum

Question 3

Find a suitable linear approximation that lets you estimate the value 10001/5 and give the estimate.

Accepted Answer

A)  L(x) = 4 +   , 3.981 
B)  L(x) = 4 -   , 4.019 
C)  L(x) = 4 +   , 3.977 
D)  L(x) = 4 +   , 3.984 
E)  L(x) = 4 -   , 4.023 
A)  L(x) = 4 +   , 3.981 
B)  L(x) = 4 -   , 4.019 
C)  L(x) = 4 +   , 3.977 
D)  L(x) = 4 +   , 3.984 
E)  L(x) = 4 -   , 4.023

Question 4

Find the equations of all horizontal asymptotes of f(x) =

Accepted Answer

A)  y = -1 and y = 5 
B)  y = -1 and y = 1 
C)  y = 3 
D)  y = -1 and y = 3 
E)  y = 1 
A)  y = -1 and y = 5 
B)  y = -1 and y = 1 
C)  y = 3 
D)  y = -1 and y = 3 
E)  y = 1

Question 5

Evaluate the limit .

Accepted Answer

A)    
B)    
C)  1 
D)    
E)    
A)    
B)    
C)  1 
D)    
E)

Question 6

Find all the roots of the equation sin x = x2.

Accepted Answer

A)  ± 0.876726 
B)  0.876726 
C)  0.876833 
D)  0, 0.876726 
E)  0, 0.876833 
A)  ± 0.876726 
B)  0.876726 
C)  0.876833 
D)  0, 0.876726 
E)  0, 0.876833

Question 7

Construct a window in the shape of a semicircle over a rectangle. If the distance around the outside of the window is 8 metres, what dimensions for the rectangle will result in the rectangle having the largest possible area?

Accepted Answer

A)  1.56 m wide and 2 m tall 
B)  1.12 m wide and 2 m tall 
C)  2 m wide and 1.5 m tall 
D)  1.56 m wide and 1.56 m tall 
E)  2 m wide and 1.12 m tall 
A)  1.56 m wide and 2 m tall 
B)  1.12 m wide and 2 m tall 
C)  2 m wide and 1.5 m tall 
D)  1.56 m wide and 1.56 m tall 
E)  2 m wide and 1.12 m tall

Question 8

The function f(x) = (   - 5)   has one critical point in the interval x > 0. Find this critical point with error within 0.005 by applying Newton's Method to an appropriate function.

Accepted Answer

A)  3.4023 
B)  3.2240 
C)  3.1278 
D)  3.4259 
E)  none of the above 
A)  3.4023 
B)  3.2240 
C)  3.1278 
D)  3.4259 
E)  none of the above

Question 9

Find the Taylor polynomial of degree 3 for the function f(x) =   cos(x/4) in powers of x -  $\pi$.

Accepted Answer

A)  1 -   (x -  $\pi$) -     +     
B)  1 -   (x -  $\pi$) +     -     
C)  1 -   (x -  $\pi$) -     +     
D)  1 -   (x -  $\pi$) +     -     
E)  1 +   (x -  $\pi$) +     +     
A)  1 -   (x -  $\pi$) -     +     
B)  1 -   (x -  $\pi$) +     -     
C)  1 -   (x -  $\pi$) -     +     
D)  1 -   (x -  $\pi$) +     -     
E)  1 +   (x -  $\pi$) +     +

Question 10

Evaluate .

Accepted Answer

A)  -1 
B)  $\infty$ 
C)  3 
D)  1 
E)  - $\infty$ 
A)  -1 
B)  $\infty$ 
C)  3 
D)  1 
E)  - $\infty$

Use Newton's Method to find the solution of the equation x + tan x = 0 on the interval [2, 3] accurate to four decimal places.

Find the extreme values of f(x) = x + cos x on [0, π].

Find a suitable linear approximation that lets you estimate the value 1000^1/5 and give the estimate.

Find the equations of all horizontal asymptotes of f(x) =

Evaluate the limit .

Find all the roots of the equation sin x = x².

Construct a window in the shape of a semicircle over a rectangle. If the distance around the outside of the window is 8 metres, what dimensions for the rectangle will result in the rectangle having the largest possible area?

The function f(x) = ( - 5) has one critical point in the interval x > 0. Find this critical point with error within 0.005 by applying Newton's Method to an appropriate function.

Find the Taylor polynomial of degree 3 for the function f(x) = $Find the Taylor polynomial of degree 3 for the function f(x) = cos(x/4) in powers of x - \pi .$ cos(x/4) in powers of x - $\pi$ .

Evaluate .

Preliminaries

Limits and Continuity

Differentiation

Transcendental Functions

Integration

Techniques of Integration

Applications of Integration

Conics, Parametric Curves, and Polar Curves

Sequences, Series, and Power Series

Vectors and Coordinate Geometry in 3-Space

Vector Functions and Curves

Partial Differentiation

Applications of Partial Derivatives

Multiple Integration

Vector Fields

Vector Calculus

Differential Forms and Exterior Calculus

Ordinary Differential Equations

Filters

Exam 5: More Applications of Differentiation

Use Newton's Method to find the solution of the equation x + tan x = 0 on the interval [2, 3] accurate to four decimal places.

Find the extreme values of f(x) = x + cos x on [0, π].

Find a suitable linear approximation that lets you estimate the value 10001/5 and give the estimate.

Find the equations of all horizontal asymptotes of f(x) =

Evaluate the limit .

Find all the roots of the equation sin x = x2.

Construct a window in the shape of a semicircle over a rectangle. If the distance around the outside of the window is 8 metres, what dimensions for the rectangle will result in the rectangle having the largest possible area?

The function f(x) = ( - 5) has one critical point in the interval x > 0. Find this critical point with error within 0.005 by applying Newton's Method to an appropriate function.

Find the Taylor polynomial of degree 3 for the function f(x) = cos(x/4) in powers of x - π\piπ .

Evaluate .

Preliminaries

Limits and Continuity

Differentiation

Transcendental Functions

Integration

Techniques of Integration

Applications of Integration

Conics, Parametric Curves, and Polar Curves

Sequences, Series, and Power Series

Vectors and Coordinate Geometry in 3-Space

Vector Functions and Curves

Partial Differentiation

Applications of Partial Derivatives

Multiple Integration

Vector Fields

Vector Calculus

Differential Forms and Exterior Calculus

Ordinary Differential Equations

Filters

Find a suitable linear approximation that lets you estimate the value 1000^1/5 and give the estimate.

Find all the roots of the equation sin x = x².

Find the Taylor polynomial of degree 3 for the function f(x) = $Find the Taylor polynomial of degree 3 for the function f(x) = cos(x/4) in powers of x - \pi .$ cos(x/4) in powers of x - $\pi$ .