Question

lim f(x)=8 and lim f(x)=8, but f(3) does not exist.
x→3⁻ x→3⁺
what can you say about lim f(x)?
x→3

lim f(x)
x→3

a. is -8
b. is 8
c. does not exist
d. is ∞

Explanation:

Step1: Recall limit definition

The limit $\lim_{x
ightarrow a}f(x)$ exists if and only if $\lim_{x
ightarrow a^{-}}f(x)=\lim_{x
ightarrow a^{+}}f(x)$.

Step2: Apply given - side limits

We are given that $\lim_{x
ightarrow 3^{-}}f(x) = 8$ and $\lim_{x
ightarrow 3^{+}}f(x)=8$. Since the left - hand limit and the right - hand limit as $x$ approaches $3$ are equal.

Answer:

B. is 8