# Math Help - Fundamental theorm of calculus

1. ## Fundamental theorm of calculus

for the first part is the answer just (cos(x))^1/2 by the Fundamental theorm of calculus part 1

for the second part i know how to calucate taylor polynoimals but this i looks abit tricky can some please help me.

Thanks

2. $T_{2,0}(x) = f(0)+f'(0)x+\frac{f''(0)}{2}x^2$

It's easy to see that $f(0)=0$.

$f'(0)=\sqrt{\cos(0)} = 1$

$f''(x) = \left(\sqrt{\cos(x)}\right)' = -\frac{\sin(x)}{2\sqrt{\cos(x)}}$, so $f''(0) = 0$

Thus $T_{2,0}(x) = x$.