# How to calculate the following limit

• Mar 22nd 2010, 07:33 PM
softwareguy
How to calculate the following limit
Can someone please explain to me the steps to get the limit of the following?

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

As $x \rightarrow 1$

Thanks.
• Mar 22nd 2010, 07:56 PM
harish21
Quote:

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

$x^4-1/x-1$

As X --> 1

Thanks.

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

Now calculate the limit as x goes to 1
• Mar 22nd 2010, 08:22 PM
softwareguy
Somehow the answer is 4. How did they get the answer 4? I don't see it...
• Mar 22nd 2010, 08:25 PM
harish21
Quote:

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 $(x^{2}+1)(x+1)$

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

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

What do you get when you multiply 2 and 2?
• Mar 22nd 2010, 08:47 PM
softwareguy
Ouch, sorry about that! I totally spaced. Thanks very much for your help!