# Thread: How to calculate the following limit

1. ## How to calculate the following limit

Can someone please explain to me the steps to get the limit of the following?

$\displaystyle \frac{x^4-1}{x-1}$

As $\displaystyle x \rightarrow 1$

Thanks.

2. Originally Posted by softwareguy
Can someone please explain to me the steps to get the limit of the following?

$\displaystyle x^4-1/x-1$

As X --> 1

Thanks.
$\displaystyle \frac{x^{4}-1}{x-1}=\frac{(x^{2}+1)(x^{2}-1)}{x-1}=\frac{(x^{2}+1)(x+1)(x-1)}{x-1}=(x^{2}+1)(x+1)$

Now calculate the limit as x goes to 1

3. Somehow the answer is 4. How did they get the answer 4? I don't see it...

4. Originally Posted by softwareguy
Somehow the answer is 4. How did they get the answer 4? I don't see it...
Did you even try this?

You are left with $\displaystyle (x^{2}+1)(x+1)$

As x goes to 1 (X--->1), the limit becomes:

$\displaystyle (1^{2}+1)(1+1) = (2)(2)$

What do you get when you multiply 2 and 2?

5. Ouch, sorry about that! I totally spaced. Thanks very much for your help!