Question 1

​Use the fourth-degree Taylor polynomial centered at zero for the function   to approximate the integral   Round your answer to nearest ten thousandth. ​

Accepted Answer

A)  ​0.4765 
B)  ​0.5065 
C)  ​0.4865 
D)  ​0.4815 
E)  ​0.2315 
A)  ​0.4765 
B)  ​0.5065 
C)  ​0.4865 
D)  ​0.4815 
E)  ​0.2315

Question 2

​Find the Taylor polynomials (centred at zero)of degree (a)1,(b)2,(c)3,and (d)4. ​
​   ​

Accepted Answer

A)  ​   ,   ,   ,   
B)  ​​   ,   ,   ,   
C)  ​​   ,   ,   ,   
D)  ​​   ,   ,   ,   
E)  ​​   ,   ,   ,   
A)  ​   ,   ,   ,   
B)  ​​   ,   ,   ,   
C)  ​​   ,   ,   ,   
D)  ​​   ,   ,   ,   
E)  ​​   ,   ,   ,

Question 3

Approximate,to three decimal places,the x-value of the point of intersection of the graphs of f(x)and g(x).Round your answer to three decimal places. ​       ​

Accepted Answer

A)  0.572 
B)  0.517 
C)  0.562 
D)  0.567 
E)  0.617 
A)  0.572 
B)  0.517 
C)  0.562 
D)  0.567 
E)  0.617

Question 4

​Test the series   for convergence for using any appropriate test. ​

Accepted Answer

A)  ​converges 
B)  ​diverges 
A)  ​converges 
B)  ​diverges

Question 5

​Find the sum of the convergent series. ​
​   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​   
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​

Question 6

​Find the radius of convergence centered at   for the following function. ​   ​

Accepted Answer

A)  ​4 
B)  ​2 
C)  ​0 
D)  ​1 
E)  ​   
A)  ​4 
B)  ​2 
C)  ​0 
D)  ​1 
E)  ​

Question 7

​Determine the convergence or divergence of the p-series   ​

Accepted Answer

A)  ​The series converges. 
B)  The series diverges. 
A)  ​The series converges. 
B)  The series diverges.

Question 8

​Determine the convergence or divergence of the following series   Use a symbolic algebra utility to verify your result. ​​

Accepted Answer

A)  ​The series diverges. 
B)  ​The series converges. 
A)  ​The series diverges. 
B)  ​The series converges.

Question 9

Find the limit of the following sequence. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)  The limit does not exist. 
A)    
B)    
C)    
D)    
E)  The limit does not exist.

Question 10

​Differentiate the series for   to find the power series for the function   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​   
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​

Question 11

​Use the fifth-degree Taylor polynomial centered at   for the function   to approximate   Round your answer to nearest thousandth. ​

Accepted Answer

A)  ​0.61 
B)  ​0.607 
C)  ​0.619 
D)  ​0.732 
E)  ​0.718 
A)  ​0.61 
B)  ​0.607 
C)  ​0.619 
D)  ​0.732 
E)  ​0.718

Question 12

​Find the radius of convergence of the power series. ​
​   ​

Accepted Answer

A)  ​0 
B)  ​10 
C)  ​20 
D)  ​100 
E)  ​   
A)  ​0 
B)  ​10 
C)  ​20 
D)  ​100 
E)  ​

Question 13

​A Taylor polynomial approximation of   is given below.Use a graphing utility to graph both functions. ​   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​   
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​

Question 14

​A Taylor polynomial approximation of   is given below.Use a graphing utility to graph both functions. ​   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​   
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​

Question 15

​Write the first five terms of the power series   ​

Accepted Answer

A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​   
A)  ​   
B)  ​   
C)  ​   
D)  ​   
E)  ​

Question 16

Find the limit of the following sequence. ​   ​

Accepted Answer

A)    
B)    
C)    
D)    
E)  The limit does not exist. 
A)    
B)    
C)    
D)    
E)  The limit does not exist.

Question 17

Approximate,to three decimal places,the x-value of the point of intersection of the graphs of f(x)and g(x).Round your answer to three decimal places. ​     ​
​   ​

Accepted Answer

A)  ​0.572 
B)  ​0.517 
C)  ​0.562 
D)  ​0.567 
E)  ​0.617 
A)  ​0.572 
B)  ​0.517 
C)  ​0.562 
D)  ​0.567 
E)  ​0.617

Question 18

Use Newton's Method to find the point on the graph of   that is closest to the point   Round your answer to three decimal places.

Accepted Answer

A)  2.973, 0.164 
B)  3.532, 0.164 
C)  2.973, 1.399 
D)  1.717, 0.164 
E)  2.973,-2.397 
A)  2.973, 0.164 
B)  3.532, 0.164 
C)  2.973, 1.399 
D)  1.717, 0.164 
E)  2.973,-2.397

Question 19

​Determine the convergence or divergence of the series   Use a symbolic algebra utility to verify your result. ​​

Accepted Answer

A)  ​The series diverges. 
B)  ​The series converges. 
A)  ​The series diverges. 
B)  ​The series converges.

Question 20

​Find the radius of convergence centered at   for the following function. ​   ​

Accepted Answer

A)  ​4 
B)  ​2 
C)  ​0 
D)  ​1 
E)  ​   
A)  ​4 
B)  ​2 
C)  ​0 
D)  ​1 
E)  ​

Use the fourth-degree Taylor polynomial centered at zero for the function to approximate the integral Round your answer to nearest ten thousandth.

Find the Taylor polynomials (centred at zero)of degree (a)1,(b)2,(c)3,and (d)4.

Approximate,to three decimal places,the x-value of the point of intersection of the graphs of f(x)and g(x).Round your answer to three decimal places.

Test the series for convergence for using any appropriate test.

Find the sum of the convergent series.

Find the radius of convergence centered at for the following function.

Determine the convergence or divergence of the p-series

Determine the convergence or divergence of the following series Use a symbolic algebra utility to verify your result.

Find the limit of the following sequence.

Differentiate the series for to find the power series for the function

Use the fifth-degree Taylor polynomial centered at for the function to approximate Round your answer to nearest thousandth.

Find the radius of convergence of the power series.

A Taylor polynomial approximation of is given below.Use a graphing utility to graph both functions.

A Taylor polynomial approximation of is given below.Use a graphing utility to graph both functions.

Write the first five terms of the power series

Find the limit of the following sequence.

Approximate,to three decimal places,the x-value of the point of intersection of the graphs of f(x)and g(x).Round your answer to three decimal places.

Use Newton's Method to find the point on the graph of that is closest to the point Round your answer to three decimal places.

Determine the convergence or divergence of the series Use a symbolic algebra utility to verify your result.

Find the radius of convergence centered at for the following function.

Functions, graphs, and Limits

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions

Probability and Calculus

Differential Equations

Filters

Exam 10: Series and Taylor Polynomials

​Use the fourth-degree Taylor polynomial centered at zero for the function to approximate the integral Round your answer to nearest ten thousandth. ​

​Find the Taylor polynomials (centred at zero)of degree (a)1,(b)2,(c)3,and (d)4. ​ ​ ​

Approximate,to three decimal places,the x-value of the point of intersection of the graphs of f(x)and g(x).Round your answer to three decimal places. ​ ​

​Test the series for convergence for using any appropriate test. ​

​Find the sum of the convergent series. ​ ​ ​

​Find the radius of convergence centered at for the following function. ​ ​

​Determine the convergence or divergence of the p-series ​

​Determine the convergence or divergence of the following series Use a symbolic algebra utility to verify your result. ​​

Find the limit of the following sequence. ​ ​

​Differentiate the series for to find the power series for the function ​

​Use the fifth-degree Taylor polynomial centered at for the function to approximate Round your answer to nearest thousandth. ​

​Find the radius of convergence of the power series. ​ ​ ​

​A Taylor polynomial approximation of is given below.Use a graphing utility to graph both functions. ​ ​

​A Taylor polynomial approximation of is given below.Use a graphing utility to graph both functions. ​ ​

​Write the first five terms of the power series ​

Find the limit of the following sequence. ​ ​

Approximate,to three decimal places,the x-value of the point of intersection of the graphs of f(x)and g(x).Round your answer to three decimal places. ​ ​ ​ ​

Use Newton's Method to find the point on the graph of that is closest to the point Round your answer to three decimal places.

​Determine the convergence or divergence of the series Use a symbolic algebra utility to verify your result. ​​

​Find the radius of convergence centered at for the following function. ​ ​

Functions, graphs, and Limits

Differentiation

Applications of the Derivative

Exponential and Logarithmic Functions

Integration and Its Applications

Techniques of Integration

Functions of Several Variables

Trigonometric Functions

Probability and Calculus

Differential Equations

Filters

Use the fourth-degree Taylor polynomial centered at zero for the function to approximate the integral Round your answer to nearest ten thousandth.

Find the Taylor polynomials (centred at zero)of degree (a)1,(b)2,(c)3,and (d)4.

Approximate,to three decimal places,the x-value of the point of intersection of the graphs of f(x)and g(x).Round your answer to three decimal places.

Test the series for convergence for using any appropriate test.

Find the sum of the convergent series.

Find the radius of convergence centered at for the following function.

Determine the convergence or divergence of the p-series

Determine the convergence or divergence of the following series Use a symbolic algebra utility to verify your result.

Find the limit of the following sequence.

Differentiate the series for to find the power series for the function

Use the fifth-degree Taylor polynomial centered at for the function to approximate Round your answer to nearest thousandth.

Find the radius of convergence of the power series.

A Taylor polynomial approximation of is given below.Use a graphing utility to graph both functions.

A Taylor polynomial approximation of is given below.Use a graphing utility to graph both functions.

Write the first five terms of the power series

Find the limit of the following sequence.

Approximate,to three decimal places,the x-value of the point of intersection of the graphs of f(x)and g(x).Round your answer to three decimal places.

Determine the convergence or divergence of the series Use a symbolic algebra utility to verify your result.

Find the radius of convergence centered at for the following function.