Question

lim f(x) = 9 and lim f(x) = 9, but f(3) does not exist.
x→3⁻\tx→3⁺
what can you say about lim f(x)?
x→3
lim f(x)
x→3
a. is ∞
b. is 9
c. does not exist
d. is - 9

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 $\lim_{x
ightarrow 3^{-}}f(x) = 9$ and $\lim_{x
ightarrow 3^{+}}f(x)=9$.

Answer:

B. is 9