Use L'Hopital's Rule to work the limits. a) \lim _{x - 2} {x^{2}-2 x}/{x^{2}-x-2} b) \lim _{x -...


Use L'Hopital's Rule to work the limits.

a){eq}\lim _{x \rightarrow 2} \frac{x^{2}-2 x}{x^{2}-x-2} {/eq}

b) {eq}\lim _{x \rightarrow \infty} \frac{1-2 x^{2}}{x^{2}+1} {/eq}

c){eq}\lim _{x \rightarrow \infty} x \ln \left(1+\frac{1}{\sqrt{x}}\right) {/eq}


In order to find the value of the given limits, we will make use of the L' Hospital's rule. This rule is applied to make the given function solvable, which is otherwise not. In this rule, we take the derivative of the numerator and the denominator terms separately.

Answer and Explanation:

a) {eq}\lim _{x \rightarrow 2} \frac{x^{2}-2 x}{x^{2}-x-2} {/eq}

Applying L'Hospital's rule, we get:

{eq}\begin{align*} \ & \ \lim _{x...

See full answer below.

Become a member to unlock this answer! Create your account

View this answer

Learn more about this topic:

What is L'Hopital's Rule?

from Math 104: Calculus

Chapter 9 / Lesson 9

Related to this Question

Explore our homework questions and answers library