Answer
See explanation
Work Step by Step
a) $\lim\limits_{x \to a} f(x) = L $
The values of $f(x)$ approach $L$ as the values of $x$ approach $a$ from both sides of $a$ while $x\neq a$.
b) $\lim\limits_{x \to a^+} f(x) = L $
The values of $f(x)$ approach $L$ as the values of $x$ approach $a$ from the right of $a$, or from values of $x$ greater than $a$.
c) $\lim\limits_{x \to a^-} f(x) = L$
The values of $f(x)$ approach $L$ as the values of $x$ approach $a$ from the left of $a$, or from values of $x$ less than $a$.
d) $\lim\limits_{x \to a} f(x) = \infty$
The values of $f(x)$ approach infinity or become arbitrarily large as $x$ gets sufficiently close to $a$ while $x\neq a$. This means there is a vertical asymptote at $x=a$.
e) $\lim\limits_{x \to \infty} f(x) = L$
The values of $f(x)$ approach and get arbitrarily close to $L$ as $x$ gets sufficiently large and approaches infinity. This means there is a horizontal asymptote at $f(x)=L$.
