Question

lim x->0 sin4x/tan2x

Answer 1

\[\lim_{x \rightarrow 0} \frac{\sin(4x)}{\tan(2x)}\]
use l'hopitals: lim x->0 f(x)/g(x) = lim x->0 f'(x)/g'(x) to get:
\[\lim_{x \rightarrow 0} \frac{4\cos(4x)}{2\sec^2(2x)}\]
then you can just plug in 0 because it is defined, and get
\[\frac{4}{2}=2\]

Answer 2

Thanks, but I haven't done calculus yet so, is there another method?

Answer 3

Not that would be easier... actually, I can't really think of anything else you can do to evaluate it, since it is undefined at 0.

Answer 4

Ok then. The topic we're doing right now is trigonometry. Do you think
\[sinx/x =0 \] can be used?

Answer 5

I suppose you can try rearranging things and using double angle identities and hope something cancels... but that's a ton more work O.o