Answer
a) $\lim\limits_{x \to -1^{-}}f(x)=1$
b) $\lim\limits_{x \to -1^{+}}f(x)=1$
c) $f(-1)=1$
d) It is continuous
Work Step by Step
a) Approaching $-1$ from the left side, we choose $x^{2}$; $\lim\limits_{x \to -1^{-}}f(x)$ $=$ $\lim\limits_{x \to -1^{-}}x^{2}=1$
b) Approaching $-1$ from the right side, we choose $1$; $\lim\limits_{x \to -1^{+}}f(x)$ $=$ $\lim\limits_{x \to -1^{+}}1=1$
c) Direct answer
d) Since, $\lim\limits_{x \to -1^{-}}f(x)$ $=$ $\lim\limits_{x \to -1^{+}}f(x)$ $=$ $f(-1)=1$, It is continuous!
