Question 1

Solve the problem.
-Use a Taylor series to estimate the integral's value to within an error of magnitude less than   .

Accepted Answer

A)  0.1974 
B)  0.1115 
C)  0.2998 
D)  0.2010 
A)  0.1974 
B)  0.1115 
C)  0.2998 
D)  0.2010 A

Question 2

Find the first four terms of the binomial series for the given function.      
-

Accepted Answer

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

Question 3

Find the series' radius of convergence.
-

Accepted Answer

A)  0 
B)  1 
C)  $\infty$, for all x 
D)  2 
A)  0 
B)  1 
C)  $\infty$, for all x 
D)  2 B

Question 4

Find the Taylor polynomial of order 3 generated by f at a.
-f(x) =   , a = 1

Accepted Answer

A)    (x) =   -   +   -   
B)    (x) =   -   +   -   
C)    (x) =   -   +   -   
D)    (x) =   -   +   -   
A)    (x) =   -   +   -   
B)    (x) =   -   +   -   
C)    (x) =   -   +   -   
D)    (x) =   -   +   -

Question 5

Solve the problem.
-Use a Taylor series to estimate the integral's value to within an error of magnitude less than   .

Accepted Answer

A)  0.0003545 
B)  0.0005487 
C)  0.0001147 
D)  0.0003323 
A)  0.0003545 
B)  0.0005487 
C)  0.0001147 
D)  0.0003323

Question 6

Use power series operations to find the Taylor series at x = 0 for the given function.      
-f(x) =     ( 8x)

Accepted Answer

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

Question 7

Find the linear approximating polynomial for the function centered at a.
-f(x) = tan x, a = 0

Accepted Answer

A)  L(x) = 0 
B)  L(x) = 5x + 1 
C)  L(x) = x 
D)  L(x) = -x 
A)  L(x) = 0 
B)  L(x) = 5x + 1 
C)  L(x) = x 
D)  L(x) = -x

Question 8

Find the Taylor polynomial of order 3 generated by f at a.
-f(x) =   , a = 3

Accepted Answer

A)    (x) = 1 + 18(x - 3) + 81   + 324   
B)    (x) = 1 + 6(x - 3) + 9   + 12   
C)    (x) = 9 + 6(x - 3) +   
D)    (x) = 9 + 6(x - 3) + 9   + 12   
A)    (x) = 1 + 18(x - 3) + 81   + 324   
B)    (x) = 1 + 6(x - 3) + 9   + 12   
C)    (x) = 9 + 6(x - 3) +   
D)    (x) = 9 + 6(x - 3) + 9   + 12

Question 9

Find the quadratic approximation of f at x = 0.
-f(x) = x

Accepted Answer

A)  Q(x) = 4   
B)  Q(x) = 1 - 2x 
C)  Q(x) = 2x 
D)  Q(x) = 1 + 2x 
A)  Q(x) = 4   
B)  Q(x) = 1 - 2x 
C)  Q(x) = 2x 
D)  Q(x) = 1 + 2x

Question 10

Find the first four terms of the binomial series for the given function.      
-

Accepted Answer

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

Question 11

Find the quadratic approximation of f at x = 0.
-f(x) = ln(cos 2x)

Accepted Answer

A)  Q(x) = 2   
B)  Q(x) = -2   
C)  Q(x) = 1 + 2   
D)  Q(x) = 1 - 2   
A)  Q(x) = 2   
B)  Q(x) = -2   
C)  Q(x) = 1 + 2   
D)  Q(x) = 1 - 2

Question 12

Find the function represented by the power series.
-

Accepted Answer

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

Question 13

Find the quadratic approximation of f at x = 0.
-f(x) =

Accepted Answer

A)  Q(x) = 4x 
B)  Q(x) = 1 +   
C)  Q(x) =   
D) Q(x) = 1 + 4x 
A)  Q(x) = 4x 
B)  Q(x) = 1 +   
C)  Q(x) =   
D) Q(x) = 1 + 4x

Question 14

Use Taylor series to evaluate the limit.
-

Accepted Answer

A)  2 
B)  1 
C)  -2 
D)  - 1 
A)  2 
B)  1 
C)  -2 
D)  - 1

Question 15

Find the interval of convergence of the series.
-

Accepted Answer

A)  -16 < x < 16 
B)  7 $\le$ x $\le$ 9 
C)  x < 16 
D)  0 $\le$ x $\le$16 
A)  -16 < x < 16 
B)  7 $\le$ x $\le$ 9 
C)  x < 16 
D)  0 $\le$ x $\le$16

Question 16

Find the Taylor polynomial of order 3 generated by f at a.
-f(x) =   + x + 1, a = 4

Accepted Answer

A)    (x) = 5 + 9(x - 4) + 13   
B)    (x) = 1 + 3(x - 4) + 3   +   
C)    (x) = 21 + 9(x - 4) +   
D)    (x) = 21 + 9(x - 4) + 9   + 21   
A)    (x) = 5 + 9(x - 4) + 13   
B)    (x) = 1 + 3(x - 4) + 3   +   
C)    (x) = 21 + 9(x - 4) +   
D)    (x) = 21 + 9(x - 4) + 9   + 21

Question 17

Find the function represented by the power series.
-

Accepted Answer

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

Question 18

Determine the interval of convergence of the power series.
-

Accepted Answer

A)    
B)  (-4, 4) 
C)  (-$\infty$, $\infty$) 
D)  x = 0 
A)    
B)  (-4, 4) 
C)  (-$\infty$, $\infty$) 
D)  x = 0

Question 19

Find the first four terms of the binomial series for the given function.      
-

Accepted Answer

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

Question 20

Find the linear approximating polynomial for the function centered at a.
-f(x) =   , a = 0

Accepted Answer

A)  L(x) =   x - 6 
B)  L(x) =   x + 6 
C)  L(x) =   x - 6 
D)  L(x) =   x + 6 
A)  L(x) =   x - 6 
B)  L(x) =   x + 6 
C)  L(x) =   x - 6 
D)  L(x) =   x + 6

Solve the problem. -Use a Taylor series to estimate the integral's value to within an error of magnitude less than .

Find the first four terms of the binomial series for the given function. -

Find the series' radius of convergence. -

Find the Taylor polynomial of order 3 generated by f at a. -f(x) = , a = 1

Solve the problem. -Use a Taylor series to estimate the integral's value to within an error of magnitude less than .

Use power series operations to find the Taylor series at x = 0 for the given function. -f(x) = ( 8x)

Find the linear approximating polynomial for the function centered at a. -f(x) = tan x, a = 0

Find the Taylor polynomial of order 3 generated by f at a. -f(x) = , a = 3

Find the quadratic approximation of f at x = 0. -f(x) = x

Find the first four terms of the binomial series for the given function. -

Find the quadratic approximation of f at x = 0. -f(x) = ln(cos 2x)

Find the function represented by the power series. -

Find the quadratic approximation of f at x = 0. -f(x) =

Use Taylor series to evaluate the limit. -

Find the interval of convergence of the series. -

Find the Taylor polynomial of order 3 generated by f at a. -f(x) = + x + 1, a = 4

Find the function represented by the power series. -

Determine the interval of convergence of the power series. -

Find the first four terms of the binomial series for the given function. -

Find the linear approximating polynomial for the function centered at a. -f(x) = , a = 0

Functions

Limits

Derivatives

Applications of the Derivative

Integration

Applications of Integration

Logarithmic, Exponential, and Hyperbolic Functions

Integration Techniques

Differential Equations

Sequences and Infinite Series

Parametric and Polar Curves

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Calculus

Filters

Exam 11: Power Series

Solve the problem. -Use a Taylor series to estimate the integral's value to within an error of magnitude less than .

Find the first four terms of the binomial series for the given function. -

Find the series' radius of convergence. -

Find the Taylor polynomial of order 3 generated by f at a. -f(x) = , a = 1

Solve the problem. -Use a Taylor series to estimate the integral's value to within an error of magnitude less than .

Use power series operations to find the Taylor series at x = 0 for the given function. -f(x) = ( 8x)

Find the linear approximating polynomial for the function centered at a. -f(x) = tan x, a = 0

Find the Taylor polynomial of order 3 generated by f at a. -f(x) = , a = 3

Find the quadratic approximation of f at x = 0. -f(x) = x

Find the first four terms of the binomial series for the given function. -

Find the quadratic approximation of f at x = 0. -f(x) = ln(cos 2x)

Find the function represented by the power series. -

Find the quadratic approximation of f at x = 0. -f(x) =

Use Taylor series to evaluate the limit. -

Find the interval of convergence of the series. -

Find the Taylor polynomial of order 3 generated by f at a. -f(x) = + x + 1, a = 4

Find the function represented by the power series. -

Determine the interval of convergence of the power series. -

Find the first four terms of the binomial series for the given function. -

Find the linear approximating polynomial for the function centered at a. -f(x) = , a = 0

Functions

Limits

Derivatives

Applications of the Derivative

Integration

Applications of Integration

Logarithmic, Exponential, and Hyperbolic Functions

Integration Techniques

Differential Equations

Sequences and Infinite Series

Parametric and Polar Curves

Vectors and the Geometry of Space

Vector-Valued Functions

Functions of Several Variables

Multiple Integration

Vector Calculus

Filters