Find the Taylor series for f(x) centered at the given value of a. (Assume that f has a power series expansion. Do not show that Rn(x)→0 . f(x)=lnx, a=

Here we just want to find the Taylor series for f(x) = ln(x), centered at the value of a (which we do not know).

Remember that the general Taylor expansion is:

for our function we have:

f'(x) =  1/x

f''(x) = -1/x^2

f'''(x) =  (1/2)*(1/x^3)

this is enough, now just let's write the series:

This is the Taylor series to 3rd degree, you just need to change the value of a for the required value.

add all the numbers and check the ones place.

the answer is 486. as the ones place is more than 4, the estimation will be the next 10 ie, 490

29 is the correct answer

step-by-step explanation: