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Find the limit. \lim_{x \rightarrow 1}\frac{5}{(x-1)^{2}}

Question:

Find the limit.

{eq}\displaystyle \lim_{x \rightarrow 1}\frac{5}{(x-1)^{2}} {/eq}

Limit:

We have a function that has a square of a linear function as a term. We have many methods to solve the limit but here we will find the right-hand limit and the left-hand limit. If they are equal then this is equal to the limit asked.

Answer and Explanation:

$$\lim_{x \rightarrow 1}\frac{5}{(x-1)^{2}}\\ $$

Finding the left hand limit:

$$\lim_{x\rightarrow 1^-} \frac{5}{(x-1)^2}\\ \lim_{h\rightarrow 0}\frac{5}{-h^2}\\ =\infty\\ $$

Finding the right hand limit:

$$\lim_{x\rightarrow 1^+} \frac{5}{(x-1)^2}\\ \lim_{h\rightarrow 0}\frac{5}{h^2}\\ =\infty $$


Learn more about this topic:

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Understanding the Properties of Limits

from Math 104: Calculus

Chapter 6 / Lesson 5
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