Answer
$a.\quad 0$
$b.\quad 0$
$c.\quad 0$
$d.\quad 0$
$e.\quad 15$
$f.\quad $does not exist.
Work Step by Step
$a.\quad $
Approaching $x=-5$ from the left, $f(x)=0,$
and $\displaystyle \lim_{x\rightarrow-5^{-}}f(x)=0$
$b.\quad $
Approaching $x=-5$ from the right, $f(x)=\sqrt{25-x^{2}},$ and
$\displaystyle \lim_{x\rightarrow-5^{+}}f(x)$=$\sqrt{25-(-5)^{2}}=0$
$c.\quad $
Both one sided limits exist, and they are equal $\Rightarrow \displaystyle \lim_{x\rightarrow-5}f(x)=0$
$d.\quad $
Approaching $x=5$ from the left, $f(x)=\sqrt{25-x^{2}}$
$\displaystyle \lim_{x\rightarrow 5^{-}}f(x)=\sqrt{25-5^{2}}=0$
$e.\quad $
Approaching $x=5$ from the right, $f(x)=3x$
$\displaystyle \lim_{x\rightarrow 5^{+}}f(x)=3(5)=15$
$f.\quad $
The one-sided limits exist, but they are not equal.
$\displaystyle \lim_{x\rightarrow 5}f(x)$ does not exist.
