Question

question 12
if $lim_{x
ightarrow3^{-}} = 2.5$, then if $lim_{x
ightarrow3} f(x)$ exists, find the value where it exists.
2.8
3
6
2.5
no correct answer choice is given.

Explanation:

Step1: Recall limit - existence condition

The limit $\lim_{x
ightarrow a}f(x)$ exists if and only if $\lim_{x
ightarrow a^{-}}f(x)=\lim_{x
ightarrow a^{+}}f(x)$. Here, we are given $\lim_{x
ightarrow 3^{-}}f(x) = 2.5$. When $\lim_{x
ightarrow 3}f(x)$ exists, the left - hand limit and the overall limit are equal.

Step2: Determine the value of the limit

Since $\lim_{x
ightarrow 3}f(x)$ exists and $\lim_{x
ightarrow 3^{-}}f(x)=2.5$, then $\lim_{x
ightarrow 3}f(x)=2.5$.

Answer:

D. 2.5