Find the limit (as x approaches 0) of (tan^2(x)) / x

Limits, differentiation, related rates, integration, trig integrals, etc.
nona.m.nona
Posts: 288
Joined: Sun Dec 14, 2008 11:07 pm
Contact:

Find the limit (as x approaches 0) of (tan^2(x)) / x

Find the limit(x approaches 0) of (tan²x)/x

I am more interested in the steps themselves, rather than the answer, because the answer is obvious (by just plugging-in values).

Martingale
Posts: 333
Joined: Mon Mar 30, 2009 1:30 pm
Location: USA
Contact:

Re: Find the limit (as x approaches 0) of (tan^2(x)) / x

nona.m.nona wrote:Find the limit(x approaches 0) of (tan²x)/x

I am more interested in the steps themselves, rather than the answer, because the answer is obvious (by just plugging-in values).

$\lim_{x\to 0}\frac{\tan^2(x)}{x}=\lim_{x\to 0}\frac{\tan(x)\tan(x)}{x}=\lim_{x\to 0}\tan(x)\cdot\lim_{x\to 0}\frac{tan(x)}{x}$

$=\lim_{x\to 0}\tan(x)\cdot\lim_{x\to 0}\frac{\sin(x)}{x}\cdot\lim_{x\to 0}\frac{1}{\cos(x)}=\cdots$

nona.m.nona
Posts: 288
Joined: Sun Dec 14, 2008 11:07 pm
Contact:

Re: Find the limit (as x approaches 0) of (tan^2(x)) / x

I keep forgetting those cos and sin limits. Thank you!