# Math Help - Limits

1. ## Limits

Let f(x) = 5-x^2, x is less than or equal to 2
(x+3)/(x-2), x>2

Find the limit of f(x) as

a) x approaches negative infinity
b) x approaches 2^-
c) x approaches 2^+
d) x approaches positive infinity

2. Hello, CalcQueen!

Let $f(x) \:= \:\begin{Bmatrix}5-x^2& & x \leq 2 \\ \\[-4mm]\dfrac{x+3}{x-2}& & x>2 \end{Bmatrix}$

Find the limit of $f(x)$ as:

$a)\;\;x \to -\infty$
$\lim_{x\,\to\,\text{-}\infty}(5-x^2) \;=\;-\infty$

$b)\;\;x \to 2^-$
$\lim_{x\to2^-}(5-x^2) \;=\;1$

$c)\;\; x \to 2^+$

$\lim_{x\to2^+}\,\frac{x+3}{x-2} \;\to\;\frac{5}{0} \:\to\: \infty$

$d)\;\;x \to +\infty$

$\lim_{x\to2^+}\,\frac{x+3}{x-2} \;=\;\lim_{x\to2^+}\,\frac{1 + \frac{3}{x}}{1 - \frac{2}{x}} \;=\;\frac{1+0}{1-0} \:=\:1$