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



{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.

Answer and Explanation:

Become a Study.com member to unlock this answer! Create your account

View this answer


{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.

$$\begin{align*} \displays...

See full answer below.

Learn more about this topic:

How to Determine the Limits of Functions


Chapter 6 / Lesson 4

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.

Related to this Question

Explore our homework questions and answers library