Question

Find the limit as x approaches 0. 1-cos3x/sin3x.

Answer 1

use l'hospitals

Answer 2

what is that?

Answer 3

It's a rule in which you differentiate the numerator and denominator to simplify a limit when the fraction is in the form of \(0 \over 0\) or \(\infty\over \infty\)

Answer 4

how do you use that rule in this problem?

Answer 5

You will keep differentiating the numerator and denominator till you stop getting \(0 \over 0\) or \(\infty \over \infty\).

Answer 6

I haven't learned what differentiating is

Answer 7

I may be breaking some math laws here but what it you divide both the top and bottom by 3x:
\[\large \frac{\frac{1-cos3x}{3x}}{\frac{sin3x}{3x}}\]
Then use the special limits for sine and cosine

Answer 8

lets do it other way then,

now just put x=0,and evaluate,
did u get that?
can u solve further?