What did I do wrong here? (expressing root x as taylor series about a=4)

[skyturnred]

Homework Statement

Here is the question:

I don't quite know what I did wrong. My method is below.

Homework Equations

The Attempt at a Solution

f(x)=√x
f'(x)=\frac{1}{2(x)^{1/2}}
f''(x)=\frac{-1}{(2)(2)(x^{3/2}}

a=4
f(a)=2
f'(a)=1/4
f''(a)=\frac{-1}{4(4^{3})^{1/2}}

so wouldn't the second taylor polynomial be what I put in the answer field above? Thanks.

 

[SammyS]

Homework Statement

Here is the question:

I don't quite know what I did wrong. My method is below.

Homework Equations

The Attempt at a Solution

f(x)=√x
f'(x)=\frac{1}{2(x)^{1/2}}
f''(x)=\frac{-1}{(2)(2)(x^{3/2}}

a=4
f(a)=2
f'(a)=1/4
f''(a)=\frac{-1}{4(4^{3})^{1/2}}

so wouldn't the second Taylor polynomial be what I put in the answer field above? Thanks.

What you have is the degree 2 term (almost). What's the sign?

Include the constant term & the linear term.

 

[skyturnred]

What you have is the degree 2 term (almost). What's the sign?

Include the constant term & the linear term.

Oh, so if it asks for T_{2} it also wants the T_{1} and the constant term as well?

Also, I see now that I somehow dropped a negative sign. Thanks!

EDIT: I just tried it and it's correct, so I answered my own question. But thanks again!