1. ## taylor polynomial error

though tutoring, i think i understand the basic taylor concept now...

Let
f (x) =x^1/2
(a) Find the Taylor polynomial
T(x) of f (x) of degree 3 centered around a = 1.
(b) Use
T(x) to find an approximation of 2^1/2

(c) Estimate the error in your approximation in part (b).

i found a to be 1+1/2(x-1) -1/8 (x-1)^2 + 1/16 (x-1)^3

should i write my answer like the above or include the factorials?

then for b i got 23/16

and i have no idea what to do for c.

2. Your taylor polynomial should be as such

$P_3=1+\frac{x-1}{2}-\frac{(x-1)^2}{8}+\frac{(x-1)^3}{16}$

Which is correct, now to approximate the error, the best thing I would do is find a power series representation of this polynomial and since this series would be an alternating series you can implement the error as I stated earlier

$|S-S_n| \le A_{n+1}$

3. honestly, all that went way over my head.. it was hard enough to figure out the taylor series for me. i need like a step by step thing explaining where everything comes from, after the polynomial that we already have. (my book is solely proofs, so it isnt the slightest help to me in this kind of instance)