Question

Use the series for f of x equals 1 over the quantity 1 plus x squared to write the series for g(x) = tan–1(x).
A. C plus x minus x cubed over 3 plus x to the 5th power over 5 minus ...
B. C plus x minus x squared over 2 plus x cubed over 3 minus ...
C. C + 2 – 2x – 3x2 –
D. None of these

Answer 1

Recall that ∫ 1/(1+x^2) dx = arctan(x)
so integrate the series for 1/(1+x^2) term by term

Answer 2

so B?

Answer 3

stop guessing and look up the series involved to confirm your work.

Answer 4

sorry i'm not guessing i'm just confused and need help.

Answer 5

1/(1+x^2) = 1 - x^2 + x^4 - x^6 + ...
integrating that, you get
∫ 1/(1+x^2) dx = x - x^3/3 + x^5/5 - x^7/7 + ...

Now, if you check the series for arctan(x), you get
arctan(x) = x - x^3/3 + x^5/5 - x^7/7 + ...

ta-daa! choice A
Now, why does it say C at the front?