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## Homework Statement

Approximate f by a Taylor polynomial with degree n at the number a.

f(x) = x^(1/2)

a=4

n=2

4<x<4.2

(This information may not be needed for this, there are two parts but I only need help on the first)

## Homework Equations

Summation [tex]f^(i) (a) * (x-a)^i / i![/tex]

## The Attempt at a Solution

Derivatives...

[tex]x^(1/2)

0.5 * x^(-1/2)

-0.25 * x^(-3/2)[/tex]

So the Taylor series of order n=2 should be...

2 + 0.25(x-4) - (1/64)(x-4)(x-4)

Now, my question...

To find the approximation of square root of x, do I just plug in 4 to that?

That would make most of the terms zero, leaving me with 2

Does this mean that whenever the Taylor series is centered at a number, the first term is the approximation?

Ugh, sorry for the failure using tex tags :( It's my first post here