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- 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?

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?