Check my answer please (Error in Taylor's)?

Question

Plz check my answer and explain if i'm wrong. thanks in advance.

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Let p(x) be the taylor poly. for f(x) = log(1-x) about a=0

How large should n be chosen to have |f(x) -p(x)| <= 10^-4

for

a) [-1/2,1/2]

b) [-1,1/2]

Answer:

I think n should be the same for a and b, since the x max is 1/2 for both.

f^(n+1)= -n!/ (1-x)^(n+1)

So, the formula: R(x) = |(x-a)^(n+1)/ (n+1)! * f^(n+1)C(x) | <= 10^-4

Plugging in f^(n+1) and simplifying, I get that

|R(x)| = |1/(n+1)| <=10^-4

which would mean that n = 9,999 ?

This seems way too large. Please let me know if it's right, thanks all.

Answer 1

Looks good, the x max in both is 1/2, so that&#039;s why you have the same n

Seems huge, huh? But good job.