Answer
(a)=0
(b)=0
(c)=0
(d)=3
Work Step by Step
(a)$\lim\limits_{x \to -2^-} F(x) =0$
As "x" is approaching to -2 from left side along the curve F(x)
therefore $F(x)=0$.
(b)$\lim\limits_{x \to -2^+} F(x) =0$
As "x" is approaching to -2 from right side along the curve F(x)
therefore $F(x)=0$.
(c)$\lim\limits_{x \to -2} F(x) =0$
By the Theorem 1.1.3
$\lim\limits_{x \to a } f(x) = L $ if and only if $\lim\limits_{x \to a ^-} f(x) = L = \lim\limits_{x \to a ^+} f(x) = L $
The relationship between one sided and two sided limits
(d)$F(-2)=3$
We do have a hole on curve at x=-2 ,so point above it represent value of F(-2) that is 3.
