Taylor series!!!! Help please!?

Question

Find first four non-zero terms of the Maclaurin series for f(x)= ln(1+x^2). Use it to find f(0.3).

Answer 1

first term:
f'(x) = 2x/(1+x^2)
f'(0) = 0 - doesn't work.

second term:
f''(x) = (2(1+x^2) - 2x * 2x) / (1 + x^2)^2 = (2-2x^2) / (1+x^2)^2
f''(0) = (2-0) / (1+0)^2 = 2 - WORKS!

now the second term of McLauren sequence:

f''(0) * x^2 / 2! = 2 * x^2 / 2 = x^2

for x=0.3, that equals 0.09

Checking with the calculator, never hurts:
ln (1 + 0.3^2) = ln (1.09) = 0.0862, so we're good

so there you go :)

Answer 2

This is very similar to a question asked by 'nosaj amazin' about an 2 hours ago. Look at my answer there.