by "undefined" , I believe you mean that the limits do not exist. if so, I agree with your results.
Here are a few limit questions that I cannot figure out.
- Lim x--> Infinity Sin(x)
- Lim x--> Infinity (Sin(x)-x)
- Lim x--> Infinity (x / Sin(x))
- Lim x--> Infinity (Sin(x) / x)
My answers;
- Undefined, since Sin(x) varies b/w -1 and 1 and the end behavior is unknown at infinity
- Undefined
- Undefined
- 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