## Related questions with answers

Question

Prove the statement using the epsilon, delta definition of limit.

$\lim _{x \rightarrow 3} \frac{x^2+x-12}{x-3}=7$

Solution

VerifiedAnswered 2 years ago

Answered 2 years ago

Step 1

1 of 2Let $\varepsilon$ be a given positive number. We have $a=3$ and $L=7$, we need to find a number $\delta$ such that

$\text{if }~~ 0\lt |x-3|\lt\delta ~~\text{ then }~~ |\dfrac{x^2+x-12}{x-3}-7|\lt\varepsilon$

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