Answer
See solution and answer
Work Step by Step
a) $h(1)=\frac{\tan(1)-1}{1^3}=0.557$
$h(0.5)=0.370$
$h(0.1)=0.335$
$h(0.05)=0.3337$
$h(0.01)=0.333347$
$h(0.005)=0.333337$
b) $\lim\limits_{x \to 0}\frac{\tan x-x}{x^3}=\frac{1}{3}$
c) $h(10^{-5})=0.333$
$h(10^{-6})=0.3$
$h(10^{-7})=0$
For very small values of x, tanx=0, so the value of h(0) became 0
d) At first glance, it looks like the limit is $\frac{1}{3}$, however, zooming in will allow you to see the distortions.
