Question

choose the best answer for the limit. if $lim_{x
ightarrow6^{-}}f(x)=lim_{x
ightarrow6^{+}}=-4$, but $f(6) = 4$, then $lim_{x
ightarrow6}f(x)$ is 4. is infinite. is - 4. does not exist.

Explanation:

Step1: Recall limit - existence rule

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: Analyze given left - hand and right - hand limits

We are given that $\lim_{x
ightarrow 6^{-}}f(x)=\lim_{x
ightarrow 6^{+}}f(x)= - 4$.

Step3: Determine the limit value

Since the left - hand limit and the right - hand limit as $x$ approaches 6 are equal, $\lim_{x
ightarrow 6}f(x)$ is equal to this common value, which is $-4$. The value of the function at $x = 6$ (i.e., $f(6)$) does not affect the limit value.

Answer:

is $-4$.