Question

choose the best answer for the limit. if $lim_{x
ightarrow5^{-}}f(x)=2$ and $lim_{x
ightarrow5^{+}}f(x)=7$, then $lim_{x
ightarrow5}f(x)$_____. if $lim_{x
ightarrow5^{-}}f(x)=2$ and $lim_{x
ightarrow5^{+}}f(x)=7$, then $lim_{x
ightarrow5}f(x)$ does not exist. is $infty$. is 2. is - 2.

Explanation:

Step1: Recall limit - existence condition

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

Step2: Compare left - hand and right - hand limits

Given $\lim_{x
ightarrow5^{-}}f(x) = 2$ and $\lim_{x
ightarrow5^{+}}f(x)=7$. Since $2
eq7$.

Answer:

does not exist.