8. (a) (10 points) Find the Taylor series centered at a = 1 of the function f(x) = x lnx-x. (Note: Here you have to comp

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8 A 10 Points Find The Taylor Series Centered At A 1 Of The Function F X X Lnx X Note Here You Have To Comp 1 (66.22 KiB) Viewed 55 times

8. (a) (10 points) Find the Taylor series centered at a = 1 of the function f(x) = x lnx-x. (Note: Here you have to compute each f(")(x) and use it as required in the expres- sion of for the Taylor series.) (b) (5 points) Find the interval of convergence of the series you found in part (a). (c) (5 points) Find the value of the Taylor series for x = e¹/2. What can you say about the value of the series at x = e? (Fact: f(x) is one of the 'good' functions-functions for which the value of the Taylor series is equal to the value of the function wherever the series converges.) What can you say about the value of the Taylor series at x = e.