Find the given limit. $$ \lim _{x \rightarrow-2} \frac{x^{2}-6}{2-x} $$ Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. $$ \lim _{x \rightarrow-2} \frac{x^{2}-6}{2-x}=\square $$ (Simplify your answer.) B. The limit does not exist.

Question

UpStudy AI · Accepted Answer

To evaluate the limit:

$$
\lim_{x \rightarrow -2} \frac{x^{2} - 6}{2 - x}
$$

Let's substitute $$ x = -2 $$ directly into the expression:

$$
\frac{(-2)^{2} - 6}{2 - (-2)} = \frac{4 - 6}{4} = \frac{-2}{4} = -\frac{1}{2}
$$

Since the substitution yields a finite value, the limit exists and is equal to $$-\frac{1}{2}$$.

**Answer:**

A. $$ \lim _{x \rightarrow-2} \frac{x^{2}-6}{2-x}=-\dfrac{1}{2} $$
The limit is $$-\frac{1}{2}$$.

Find the given limit. \( \lim _{x \rightarrow-2} \frac{x^{2}-6}{2-x} \) Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. \( \lim _{x \rightarrow-2} \frac{x^{2}-6}{2-x}=\square \) (Simplify your answer.) B. The limit does not exist.

Real Tutor Solution

Answer

Solution

Mind Expander

Related Questions

Latest Calculus Questions