L’Hôpital’s rule to evaluate the 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 the 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

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

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 the 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**

Now here I have to evaluate the limit of the function

So this means here

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

So this means here

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.

Now I’ll give another example.

**Example 3**

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

”

**Solution**

Now here I have to evaluate the limit of the function

So this means here

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

Therefore I get

So this is an indeterminate form like examples 1 and 2.

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

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

Dear friends, this is the end of 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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