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Exam 11: Taylor Polynomials and Infinite Series

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Exam 1: Preliminaries183 Questionsadd course
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Exam 3: Differentiation309 Questionsadd course
Exam 4: Applications of the Derivative152 Questionsadd course
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Exam 11: Taylor Polynomials and Infinite Series110 Questionsadd course
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Use the Newton method to approximate the indicated zero of the function. Continue with the iteration until two successive approximations differ by less than 0.0001. Round your answer to five decimal places, if necessary. ​ The zero of Use the Newton method to approximate the indicated zero of the function. Continue with the iteration until two successive approximations differ by less than 0.0001. Round your answer to five decimal places, if necessary. ​ The zero of between and , . between Use the Newton method to approximate the indicated zero of the function. Continue with the iteration until two successive approximations differ by less than 0.0001. Round your answer to five decimal places, if necessary. ​ The zero of between and , . and Use the Newton method to approximate the indicated zero of the function. Continue with the iteration until two successive approximations differ by less than 0.0001. Round your answer to five decimal places, if necessary. ​ The zero of between and , . , Use the Newton method to approximate the indicated zero of the function. Continue with the iteration until two successive approximations differ by less than 0.0001. Round your answer to five decimal places, if necessary. ​ The zero of between and , . .

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Question 1
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1.91515

Consider the function Consider the function at . ​ Find the Taylor series of the function at the indicated point. ​ __________ ​ Find its radius of convergence. ​ __________ ​ Find the interval of convergence. ​ __________ at Consider the function at . ​ Find the Taylor series of the function at the indicated point. ​ __________ ​ Find its radius of convergence. ​ __________ ​ Find the interval of convergence. ​ __________ . ​ Find the Taylor series of the function at the indicated point. ​ __________ ​ Find its radius of convergence. ​ __________ ​ Find the interval of convergence. ​ __________

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Question 2
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Consider the function Consider the function . ​ Find the Taylor series of the function at the indicated point. ​ __________ ​ Find its radius of convergence. ​ __________ ​ Find the interval of convergence. ​ __________ . ​ Find the Taylor series of the function at the indicated point. ​ __________ ​ Find its radius of convergence. ​ __________ ​ Find the interval of convergence. ​ __________

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Question 3
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Show that the series is divergent. Show that the series is divergent.

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Question 4

Find P​3(x), the third Taylor polynomial of the following function at the indicated point. ​ Find P​<sub>3</sub>(x), the third Taylor polynomial of the following function at the indicated point. ​ at ​ Express any non-integer coefficients as reduced fractions. at Find P​<sub>3</sub>(x), the third Taylor polynomial of the following function at the indicated point. ​ at ​ Express any non-integer coefficients as reduced fractions. ​ Express any non-integer coefficients as reduced fractions.

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Question 5

Consider the series ​ Consider the series ​ . ​ Determine whether the geometric series converges or diverges. ​ If it converges, find its sum. . ​ Determine whether the geometric series converges or diverges. ​ If it converges, find its sum.

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Question 6

Consider the function Consider the function at . ​ Use the second Taylor polynomial to approximate . Round the answer to six decimal places, if necessary. ​ __________ ​ Find a bound for the error in the approximation. Round the answer to five decimal places, if necessary. ​ __________ at Consider the function at . ​ Use the second Taylor polynomial to approximate . Round the answer to six decimal places, if necessary. ​ __________ ​ Find a bound for the error in the approximation. Round the answer to five decimal places, if necessary. ​ __________ . ​ Use the second Taylor polynomial to approximate Consider the function at . ​ Use the second Taylor polynomial to approximate . Round the answer to six decimal places, if necessary. ​ __________ ​ Find a bound for the error in the approximation. Round the answer to five decimal places, if necessary. ​ __________ . Round the answer to six decimal places, if necessary. ​ Consider the function at . ​ Use the second Taylor polynomial to approximate . Round the answer to six decimal places, if necessary. ​ __________ ​ Find a bound for the error in the approximation. Round the answer to five decimal places, if necessary. ​ __________ __________ ​ Find a bound for the error in the approximation. Round the answer to five decimal places, if necessary. ​ __________

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Question 7

Estimate the value of the radical by using three iterations of the Newton-Raphson method with the indicated initial guess for the function. Round your answer to six decimal places, if necessary. ​ Estimate the value of the radical by using three iterations of the Newton-Raphson method with the indicated initial guess for the function. Round your answer to six decimal places, if necessary. ​ ; ; ; Estimate the value of the radical by using three iterations of the Newton-Raphson method with the indicated initial guess for the function. Round your answer to six decimal places, if necessary. ​ ; ; ; Estimate the value of the radical by using three iterations of the Newton-Raphson method with the indicated initial guess for the function. Round your answer to six decimal places, if necessary. ​ ; ;

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Question 8

Use the sixth-degree Taylor polynomial to approximate ​ Use the sixth-degree Taylor polynomial to approximate ​ ​ ​

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Question 9

Estimate the value of the radical by using three iterations of the Newton-Raphson method with the indicated initial guess for the function. Round your answer to six decimal places, if necessary. ​ Estimate the value of the radical by using three iterations of the Newton-Raphson method with the indicated initial guess for the function. Round your answer to six decimal places, if necessary. ​

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Question 10

Consider the series ​ Consider the series ​ . ​ Determine whether the geometric series converges or diverges. ​ If it converges, find its sum. . ​ Determine whether the geometric series converges or diverges. ​ If it converges, find its sum.

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Question 11

Consider the series Consider the series . ​ Find the radius of convergence of the power series. ​ __________ ​ Find the interval of convergence of the power series. ​ __________ . ​ Find the radius of convergence of the power series. ​ __________ ​ Find the interval of convergence of the power series. ​ __________

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Question 12

Consider the series ​ Consider the series ​ . ​ Determine whether the geometric series converges or diverges. ​ If it converges, find its sum. . ​ Determine whether the geometric series converges or diverges. ​ If it converges, find its sum.

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Question 13

Write down the first five terms of the sequence. ​ Write down the first five terms of the sequence. ​

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Question 14

A division manufactures the "Futura" model microwave oven. Given that the daily cost of producing these microwave ovens (in dollars) obeys the rule ​ A division manufactures the Futura model microwave oven. Given that the daily cost of producing these microwave ovens (in dollars) obeys the rule ​ ​ where x stands for the number of units produced, find the level of production that minimizes the daily average cost per unit. Round your answer to the nearest integer. ​ __________ units per day ​ where x stands for the number of units produced, find the level of production that minimizes the daily average cost per unit. Round your answer to the nearest integer. ​ __________ units per day

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Question 15

Consider the series Consider the series . ​ Find the radius of convergence of the power series. ​ __________ ​ Find the interval of convergence of the power series. ​ __________ . ​ Find the radius of convergence of the power series. ​ __________ ​ Find the interval of convergence of the power series. ​ __________

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Question 16

The altitude (in feet) of a rocket t sec into flight is given by ​ The altitude (in feet) of a rocket t sec into flight is given by ​ ​ Find the time T when the rocket hits Earth. Round your answer to the nearest second. ​ __________ sec ​ Find the time T when the rocket hits Earth. Round your answer to the nearest second. ​ The altitude (in feet) of a rocket t sec into flight is given by ​ ​ Find the time T when the rocket hits Earth. Round your answer to the nearest second. ​ __________ sec __________ sec

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Question 17

Consider the series ​ Consider the series ​ . ​ Find the values of x for which the series converges. ​ Find the sum of the series where it is convergent . ​ Find the values of x for which the series converges. ​ Find the sum of the series where it is convergent

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Question 18

Find the general term Find the general term of the sequence. ​ of the sequence. ​ Find the general term of the sequence. ​

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Question 19

Determine whether the following series is convergent or divergent. ​ Determine whether the following series is convergent or divergent. ​

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Question 20
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