Question

consider the following function and graph. (f(x)=\frac{1}{x + 3}) determine whether (f(x)) approaches (infty) or (-infty) as (x) approaches (-3) from the left and from the right. (a) (lim_{x
ightarrow - 3^{-}}f(x)) (b) (lim_{x
ightarrow - 3^{+}}f(x))

Explanation:

Step1: Analyze left approach

\( x \to -3^- \implies x+3 \to 0^- \implies \frac{1}{x+3} \to -\infty \)

Step2: Analyze right approach

\( x \to -3^+ \implies x+3 \to 0^+ \implies \frac{1}{x+3} \to \infty \)

Answer:

(a) \( -\infty \)
(b) \( \infty \)