Question

(i) Why can’t we compute the Taylor polynomial of ln(x) about a = 0? (ii) Write out the Taylor polynomial at x, about a = 0, of degree 5 for f (x) = ln(1 + x), along with the corresponding remainder. (iii) Give an upper bound for this remainder when x = 0, x = 0.01 and x = 0.1. (iv) How does the derivative of the Taylor polynomial found in part (ii) compare to the fourth-order Taylor polynomial about a = 0 for f (x) = 1/(1 + x)?

Name: i why cant we compute the taylor polynomial of lnx about a 0 ii write out the taylor polynomial at x about a 0 of degree 5 for f x ln1 x along with the corresponding remainder iii give an up 99784
Uploaded: 2021-05-22T19:46:43-08:00
Duration: 3 min 15 s
Channel: Wendi Zhao
Description: i why cant we compute the taylor polynomial of lnx about a 0 ii write out the taylor polynomial at x about a 0 of degree 5 for f x ln1 x along with the corresponding remainder iii give an up 99784

          (i) Why can’t we compute the Taylor polynomial of ln(x) about a = 0?  (ii) Write out the Taylor polynomial at x, about a = 0, of degree 5 for f (x) = ln(1 + x), along with the corresponding remainder.  (iii) Give an upper bound for this remainder when x = 0, x = 0.01 and x = 0.1.  (iv) How does the derivative of the Taylor polynomial found in part (ii) compare to the fourth-order Taylor polynomial about a = 0 for f (x) = 1/(1 + x)?

Added by Edward F.

Elementary and Intermediate Algebra

Alan S. Tussy, R. David Gustafson 5th Edition

Instant Answer

Solved by Expert Wendi Zhao

05/22/2021

Step 1

Therefore, we cannot compute the Taylor polynomial of ln(x) about a = 0 because it is not defined at that point. Show more…

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(i) Why can’t we compute the Taylor polynomial of ln(x) about a = 0? (ii) Write out the Taylor polynomial at x, about a = 0, of degree 5 for f (x) = ln(1 + x), along with the corresponding remainder. (iii) Give an upper bound for this remainder when x = 0, x = 0.01 and x = 0.1. (iv) How does the derivative of the Taylor polynomial found in part (ii) compare to the fourth-order Taylor polynomial about a = 0 for f (x) = 1/(1 + x)?