The Taylor
series of f , centered at a , is
f(x) = f(a) + f'(a) (x-a) + \frac12 f''(a) (x-a)^2 + \cdots

In this problem you will use this formula with

This is the best value of

The first approximation is

You might remember this as the linear approximation from Calculus I.
The quadratic approximation to

Warning! WeBWorK might have marked those approximations as correct even if they are wrong.
This is because WeBWorK marks an answer correct if it is within 0.1 per cent of the correct answer.
A good way to see if you did it right it to check the errors of the approximations.
You don't need a calculator for this part either, since WeBWorK can do the calculations for you.

The error (positive or negative) of the first approximation is

The error (positive or negative) of the second approximation is

You can earn partial credit on this problem.