Find the limit $\lim _{x \rightarrow 3} \frac{x^{2}-x-6}{x-3}$ , if it exists.
A) 3
B) 5
C) 2
D) Does not exist

Name: Find the limit $\lim _{x \rightarrow 3} \frac{x^{2}-x-6}{x-3}$ , if it exists. A) 3 B) 5 C) 2 D) Does not exist
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Question

Quizplus · Accepted Answer

We can factor the numerator to get $\frac{(x-3)(x+2)}{x-3}$. Notice that when $x\neq3$, we can cancel out the factor of $x-3$ to get $x+2$. Therefore, if the limit exists, it must be equal to the limit of $x+2$ as $x$ approaches 3. This limit is simply 5, so the answer is B.

Find the Limit lim⁡x→3x2−x−6x−3\lim _{x \rightarrow 3} \frac{x^{2}-x-6}{x-3}limx→3​x−3x2−x−6​ , If It Exists

Find the Limit $\lim _{x \rightarrow 3} \frac{x^{2}-x-6}{x-3}$ , If It Exists