# Evaluate lim_(x -> 3) (2x^2 + 10x - 48)/(x^2 - 7x + 12)

## Question:

Evaluate

{eq}\displaystyle \lim_{x \rightarrow 3} \frac{2x^{2} + 10x - 48}{x^{2} - 7x + 12} {/eq}

## Evaluation of a Limit:

To solve this problem, we need to understand evaluation of a limit using the factorization method:

Suppose we have to find {eq}\displaystyle \lim_{x \to a} \frac{f(x)}{g(x)} \ \ \ \left ( \frac{0}{0} \text{ form } \right ) {/eq}

To compute this limit, we factorize the numerator and denominator and then plug in {eq}x = a {/eq}.

If we get a meaningful number, then that number is the required limit. Otherwise, we repeat this process until we get a meaningful number.

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Given:

{eq}\displaystyle \lim_{x \to 3 } \frac{2 x^2 + 10 x - 48}{x^2 - 7 x + 12} \\ {/eq}

We will solve step by step.

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How to Determine the Limits of Functions

from

Chapter 6 / Lesson 4
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You know the definition of a limit. You know the properties of limits. You can connect limits and continuity. Now use this knowledge to calculate the limits of complex functions in this lesson.