# Limit of trig functions

• Jonas

#### Jonas

Homework Statement
Can lim x-> infinity sin(ln(x)) /cos(sqrt(x)) be evaluated with L'Hôpitals rule?
Relevant Equations
lim x→∞ sin(ln(x))/cos(√x)
Hello.
Sin and cos separately oscillates between [-1,1] so the limit of each as x approach infinity does not exist.
But can a quotient of the two acutally approach a certain value?
lim x→∞ sin(ln(x))/cos(√x) has to be rewritten if L'hôp. is to be applied but i can't seem to find a way to rewrite it to get a meaningful answer. Ofc i tried wolframalpha who states that it approaches + and - infinity which made me even more confused since i would normally interpret that as the limit does not exist?

The function isn't defined where the denominator is zero. And, in any case, if you analyse those points you'll see the problem.

It's simpler if you let ##y = \sqrt x## and take ##y \rightarrow \infty##.

Jonas
You should look at the specific conditions where L'Hopital's rule can be used and see if those conditions are met. I suggest that you carefully review the statement of L'Hopital's rule. If you find one condition that is not met, state that condition and show that it is not met.

Jonas and jedishrfu