$\text { Use the graph to find } \lim _{x \rightarrow 2} \frac{3 x^{2}-12}{x-2}$

A) 12
B) $ \infty $
C) 6
D) 0
E) limit does not exist

Question

$\text { Use the graph to find } \lim _{x \rightarrow 2} \frac{3 x^{2}-12}{x-2}$

A) 12 
B) $ \infty $ 
C) 6 
D) 0 
E) limit does not exist

Quizplus · Accepted Answer

From the graph, we can see that as $x$ approaches 2 from both sides, the function approaches a vertical asymptote at $x=2$. Therefore, the limit does not exist. However, we can use the limit laws to find the limit of the simplified function as $x$ approaches 2:

$$\lim_{xightarrow 2}\frac{3x^2-12}{x-2}=\lim_{xightarrow 2}\frac{3(x-2)(x+2)}{x-2}=\lim_{xightarrow 2}3(x+2)=\boxed{	extbf{(A) }12}$$

Note that this is not the limit of the original function, but rather the limit of the simplified function, which is equal to the original function for all $x
eq 2$.

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$\text { Use the graph to find } \lim _{x \rightarrow 2} \frac{3 x^{2}-12}{x-2}$