Question

Limit X-->0 Xcsc(3x)/cot(4x) ?

Answer 1

If you look at it this way xtan(4x)/sin(3x) you get 0/0 indeterminite form

Answer 2

??

Answer 3

I think @Xavier is suggesting a way to solve it with l'Hôpital's Rule.
The way he has rewritten it, can also be used to calculate the limit without l'Hôpital, using the standard limit sinx/x.

Does this ring a bell?

Answer 4

ok i'll try to solve it bu this way

Answer 5

Success! Ask again if something doesn't work out...

Answer 6

thanks

Answer 7

Hey plz solve it for me :)

Answer 8

You have: \[\lim_{x \rightarrow 0}\tan 4x \cdot \frac{ x }{ \sin3x }=\lim_{x \rightarrow 0}\tan 4x \cdot \lim_{x \rightarrow 0}\frac{ x }{ \sin3x }\]
Now it's clear that \(lim_{x \rightarrow 0} tan4x=0\), so if the other limit exists, (i.e. is not infinity), then we're done.

What can you say about that second limit?

Answer 9

Doesn't it look suspiciously like the well-known standard limit: \[\lim_{x \rightarrow 0}\frac{\sin x}{x}=1\]

Answer 10

ok thank you very much