1. ## Limits

I'm relearning all my calculus after not using it for years. I'm starting fresh with limits and I have a limit question.

Please find the limit as s approaches a of (s^4 - a^4)\(s^2 - a^2). At first glance it looks like that when you plug in a to the s term then the limit is 0/0. However my book is saying the answer is 2a^2. How do they get to this answer?

2. Originally Posted by MrJoe2000
I'm relearning all my calculus after not using it for years. I'm starting fresh with limits and I have a limit question.

Please find the limit as s approaches a of (s^4 - a^4)\(s^2 - a^2). At first glance it looks like that when you plug in a to the s term then the limit is 0/0. However my book is saying the answer is 2a^2. How do they get to this answer?
The numerator is the difference of squares

$\displaystyle s^4 - a^4=(s^2)^2-(a^2)^2=(s^2-a^2)(s^2+a^2)$

Now reduce the fraction to get $(s^2+a^2)$