Answer
a) $\lim\limits_{x \to 0^{-}}G(x) = 1$
b) $\lim\limits_{x \to 0^{+}}G(x) = 1$
c) $\lim\limits_{x \to 0}G(x) = 1$
d) $G(0) = 0$
Work Step by Step
a) From the left hand side, the function trends towards (0,1)
b) The function is symmetrical about $x=0$, so from the right hand side, the function also trends towards (0,1)
c) The left hand side limit and right hand side limits are equal, so the overall limit exists and is equal to 1.
d) Since the function has a discontinuity at $x=0$, the function output is different. From the graph, we see that its value is 0.
