Question

Hello there! I need help with this Calculus problem (Senior in highschool taking Calculus). I'd appreciate any help and if you could break down the steps it would be great!

Answer 1

Given data:

The expression for the given function is,

`\begin{gathered} f(x)=\sin x,\text{ x<0} \\ =\text{ x x}\ge0 \end{gathered}`

The expression for the right hand derivative of the given function is,

`\begin{gathered} \lim _(h\to0)\text{ }(f(0+h)-f(0))/(h)=\lim _(h\to0)\text{ }(h-0)/(h) \\ \\ =1 \end{gathered}`

The expression for the left hand derivative of the given function is,

`\begin{gathered} \lim _(h\to0)\text{ }(f(0-h)-f(0))/(-h)=\lim _(h\to0)\text{ }(\sin (-h)-0)/(h) \\ =\lim _(h\to0)\text{ -}(\sin h)/(-h) \\ =1 \end{gathered}`

The given function is continuous as well as differentiable at x=0.

Thus, the