# Power series expansions - which is imossible

Which of the following expansions is impossible?

a $$\sqrt{x-1}$$ in powers of x

b $$\sqrt{x+1}$$ in powers of x

c $$ln(x)$$ in powers of (x-1)

d $$tanx$$ in powers of (x-\pi / 4 )

e $$ln(1-x)$$ in powers of x

What are htey asking and how do i do this? the answer is A by the way

## Answers and Replies

Mark44
Mentor

"In powers of (x - a)" means that x will be close to a, and that the function and its derivatives will be evaluated at a. Which of the functions above are defined at a (which will be 0, or 1, or pi/4 in these problems)?

So for a, x=0, and that is an imaginary result. Is this the same thing as saying it is centered around a?

Thank you.

Mark44
Mentor

So for a, x=0, and that is an imaginary result. Is this the same thing as saying it is centered around a?

Thank you.
If a = 0, it is.