L’Hôpital’s rule to evaluate limits of functions. Today it’s all about L’Hôpital’s rule to evaluate limits of functions. Have a look!

### L’Hôpital’s rule to evaluate limits of functions

Well, the first question is: what is L’Hôpital’s rule?

Now here I try to explain it in a simple way.

Suppose I have function like

Now I have to find the limiting value of this function when approaches 0.

In mathematics, it will be like

This means the limiting value of this function will be

Now, suppose both and are zero.

That means the limiting value of the function is

Now this is an indeterminate form.

So here comes L’Hôpital’s rule.

L’Hôpital’s rule says for this kind of form, the limiting value of the function will be

Now suppose both and are zero.

Then the limiting value of the function will be

And it will continue like this till some determinate form shows up.

Here I give some examples. I think that will help.

#### Examples of L’Hôpital’s rule to evaluate limits of functions

Disclaimer: None of these examples is mine. I have chosen these from some book or books. I have also given the due reference at the end of the post.

So here are the examples.

##### Example 1

According to Stroud and Booth (2013)* “Evaluate:

”

##### Solution

Here I have to evaluate the limit of the function when approaches 1.

So this means here and .

First of all, I’ll find out the value of .

Therefore I get

Read more: formulas for logarithmic and hyperbolic functions

So this is an indeterminate form.

Now I’ll apply L’Hôpital’s rule to find out the limit of the function.

This means I’ll differentiate both top and bottom functions with respect to .

Thus it will be

Hence I can conclude that this is the answer to this example.

Here comes the next example.

##### Example 2

According to Stroud and Booth (2013)* “Evaluate:

”

##### Solution

Here I have to evaluate the limit of the function when approaches 0.

So this means here and .

First of all, I’ll find out the value of .

Therefore I get

So this is an indeterminate form.

Now I’ll apply L’Hôpital’s rule to find out the limit of the function.

This means I’ll differentiate both top and bottom functions with respect to .

Thus it will be

But this is also an indeterminate form.

Again I’ll differentiate both top and bottom functions with respect to .

Thus it will be

Hence I can conclude that this is the answer to this example.

Dear friends, this is the end of my today’s post. Thank you very much for reading this. Please let me know how you feel about it. Soon I will be back again with a new post. Till then, bye, bye!!

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