a. Explanation Given: The function f ( x ) = 1 + x . Result used: The n th-order Taylor polynomial centered at a is as follows, p n ( x ) = f 0 ( a ) 0 ! ( x − a ) 0 + f ′ ( a ) 1 ! ( x − a ) 1 + f ″ ( a ) 2 ! ( x − a ) 2 + ⋯ + f n ( a ) n ! ( x − a ) n . Calculation: The n th-order Taylor polynomial centered at a = 0 is as follows, p n ( x ) = f ( 0 ) + f ′ ( 0 ) 1 ! ( x ) + f ″ ( 0 ) 2 ! ( x ) 2 + ⋯ + f n ( 0 ) n ! ( x ) n (1) The first derivative of f ( x ) = 1 + x is computed as follows, f ′ ( x ) = d d x ( 1 + x ) = 1 2 1 + x Substitute 0 for x in the above equation. f ′ ( 0 ) = 1 2 1 + 0 = 1 2 The second derivative of f ( x ) = 1 + x is computed as follows, f ″ ( x ) = d d x ( 1 2 1 + x ) = 1 2 ⋅ d d x ( 1 1 + x ) = 1 2 ( − 1 2 ( 1 + x ) 3 2 ) = − 1 4 ( 1 + x ) 3 2 Compute f ″ ( 0 ) as follows b. To determine To make: The table for approximations and absolute error.

Calculus, Single Variable: Early Transcendentals (3rd Edition)

3rd Edition

ISBN: 9780134766850

Author: William L. Briggs, Lyle Cochran, Bernard Gillett, Eric Schulz

Publisher: PEARSON

See similar textbooks

Videos

Question

Chapter 11, Problem 12RE

To determine

To find: The nth-order Taylor polynomial of order n=1 and 2 centered at 0.

To determine

To make: The table for approximations and absolute error.

Expert Solution & Answer

Want to see the full answer?

Check out a sample textbook solution

See solution

Chapter 11, Problem 11RE

Chapter 11, Problem 13RE

Students have asked these similar questions

practice for test please help!

X MAT21 X MindTa X A 26308 X Answer X M9 | C X 10 EKU-- × E DNA S X H. pyle x C static/nb/ui/evo/index.html?elSBN=9780357038406&id=339416021&snapshotld=877369& CENGAGE MINDTAP nctions, Limits, and the Derivative In Exercises 15, 16, 17, 18, 19, and 20, refer to the graph of the function f and determine whether each statement is true or false. -3-2-1 4- 3+ y= f(x) 2 1+ x 1 2 3 4 5 6 AA a

Chapter 11 Solutions

Calculus, Single Variable: Early Transcendentals (3rd Edition)

Ch. 11.1 - Verify that p3 satisfies p3(k)(a)=f(k)(a), for k =...Ch. 11.1 - Prob. 2QC Ch. 11.1 - Prob. 3QC Ch. 11.1 - Write out the next two Taylor polynomials p4 and...Ch. 11.1 - Prob. 5QC Ch. 11.1 - Prob. 6QC Ch. 11.1 - Suppose you use a second-order Taylor polynomial...Ch. 11.1 - Does the accuracy of an approximation given by a...Ch. 11.1 - The first three Taylor polynomials for f(x)=1+x...Ch. 11.1 - Prob. 4E

Knowledge Booster

$Calculus$

Learn more about

Need a deep-dive on the concept behind this application? Look no further. Learn more about this topic, calculus and related others by exploring similar questions and additional content below.

The n th-order Taylor polynomial of order n = 1 and 2 centered at 0.

Solution Summary: The author calculates the n th-order Taylor polynomial of order n=1and 2 centered at 0. The first derivative of f(x)=

Videos

To find: The nth-order Taylor polynomial of order n=1 and 2 centered at 0.

To make: The table for approximations and absolute error.

Want to see the full answer?

Chapter 11 Solutions