Originally Posted by
Maziana Find the limit of x(tan(8/x)) as it approaches infinity.
If I plug in infinity, I get (infinity * 0) so the problem is an indeterminate form.
So I find the limit of tan(8/x) / (1/x). This is (0 * 0) so I can use l'Hospital's rule:
sec^2(8/x)(-8x^-2) / 1
That still is (0 * 0), so I can use l'Hospital's again. I get:
(16x^-3) (2sec(8/x)(-8x^-2)
At this time I realize that this doesn't look like it's helping me, so I probably did something wrong. Can someone look over my work, tell me if I'm on the right track, and if not, tell me what I did wrong? Thanks.