Approximate f by a Taylor polynomial with degree n at the number a.
f(x) = x^(1/2)
(This information may not be needed for this, there are two parts but I only need help on the first)
Summation [tex]f^(i) (a) * (x-a)^i / i![/tex]
The Attempt at a Solution
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