# Thread: Limits at infinity of Trigonometric Functions

1. ## Limits at infinity of Trigonometric Functions

Here are a few limit questions that I cannot figure out.
1. Lim x--> Infinity Sin(x)
2. Lim x--> Infinity (Sin(x)-x)
3. Lim x--> Infinity (x / Sin(x))
4. Lim x--> Infinity (Sin(x) / x)

1. Undefined, since Sin(x) varies b/w -1 and 1 and the end behavior is unknown at infinity
2. Undefined
3. Undefined
4. Zero as x approaches infinity 1/x approaches zero.

Please help without using L'Hopital's Rule as we have not yet studied that in Calculus. Thank you

2. by "undefined" , I believe you mean that the limits do not exist. if so, I agree with your results.

3. Originally Posted by skeeter
by "undefined" , I believe you mean that the limits do not exist. if so, I agree with your results.
Yes, I should have used "does not exit", which I believe is the proper term. Thanks anyways.

4. Originally Posted by skeeter
by "undefined" , I believe you mean that the limits do not exist. if so, I agree with your results.
actually lim x--> infinity ( sin(x) - x) is negative infinity. Can be proven using the squeeze theorem.

5. Originally Posted by bilalsaeedkhan
actually lim x--> infinity ( sin(x) - x) is negative infinity. Can be proven using the squeeze theorem.
does a limit exist if it is infinite? if so, then I guess they should start posting these on the Autobahn ...

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