1. ## Limits

How does

lim (x --> 0) [tan^2(4x)] / (2x)^2

equal 4?

2. ## Re: Limits

It doesn't unless you wrote the problem wrong.

3. ## Re: Limits

Originally Posted by SlipEternal
It doesn't unless you wrote the problem wrong.
I did... I have corrected my mistake.

4. ## Re: Limits

Then, are you familiar with the limit:

Limit (x -> 0) sin x / x = 1?

Now, tan^2(4x) / (2x)^2 = [sin(4x)/(4x)] * [sin(4x)/(4x)] * [4/cos^2(4x)]

Use the product rule. As x approaches zero, so does 4x, so the limit can be broken up as the product of three limits. The first two will evaluate to 1 and the last will evaluate to 4.

5. ## Re: Limits

Originally Posted by SlipEternal
Then, are you familiar with the limit:

Limit (x -> 0) sin x / x = 1?

Now, tan^2(4x) / (2x)^2 = [sin(4x)/(4x)] * [sin(4x)/(4x)] * [4/cos^2(4x)]

Use the product rule. As x approaches zero, so does 4x, so the limit can be broken up as the product of three limits. The first two will evaluate to 1 and the last will evaluate to 4.
Got it. Thank you.