The Taylor series for $f(x) = \sqrt{100 + x}$ at $a = 0$ is $\displaystyle \sum_{n=0}^\infty c_n( x )^n.$
Find the first few coefficients.
$c_0 =$
$c_1 =$
$c_2 =$
$c_3 =$
Find the error in approximating $\sqrt{102} = f(2)$ using the third degree Taylor polynomial of $f$ at $a = 0 .$
That is, find the error of the approximation $\sqrt{102} \approx T_3(2)$.
The error is