Q. 44 - Calculus

Question

Calculate each limit in Exercises 35–80.  

$\underset{x\to 2}{lim}\frac{x+1}{{(x-2)}^2}$

Step-by-Step Solution

Answer

The limit is $\infty$.

Step 1. Given Information:

Given expression: $\underset{x\to 2}{lim}\frac{x+1}{{(x-2)}^2}$

We want to find the limit of given expression.

Step 2. Solution:

Since the numerator is positive and the denominator ${(x-2)}^2$ approaches zero and is greater than zero for x near 2 on both sides, the function increases without bound.

Hence the limit is not defined i.e. $\infty$.