Limit as x -> 0 of (x^2 + 2)/(x + 1) using L'Hôpital's rule

Step by step

The question

Question: find the limit as x → 0 of (x² + 2)/(x + 1).

1 Put the number in

Put 0 in place of x.

The top is 2, and the bottom is 1.

The bottom is not 0, so there is no problem here.

Careful!

L'Hôpital's rule is only for 0/0, or infinity over infinity.

Here it would give 0, which is wrong.

So the limit is just the value: 2.

2 Check

Let's check with a calculator, with x very close to 0.

x = −0.01 gives about 2.0203.

And x = 0.01 gives about 1.9803.

Both are close to 2.

Right!

Let's look back.

First: put the number in.

Last: check.