- #1

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- Homework Statement:
- Find the limit of the sequence as n approaching infinity.

- Relevant Equations:
- lim n-->infty n sin (1/n)

I tried to substitution n = infinity so I got (infinity)*sin (1/infinity). I thought 1/infinity is approaching zero. So, sin (1/infinity) is same with sin (0). With these idea, my solution is lim n--> infinity n sin(1/n) = 0.

But, the answer book say that the answer is 1.

I tried another method with L'Hopital rule and came with 0/0 form.

So, here is my question:

1. Why my answer isn't valid? Isn't okay that I use sin (1/infinity) = 0?

2. Are there any methods beside the L'Hopital rule and "ln" strategic to find a limit?

Thanks a bunch pals.

But, the answer book say that the answer is 1.

I tried another method with L'Hopital rule and came with 0/0 form.

So, here is my question:

1. Why my answer isn't valid? Isn't okay that I use sin (1/infinity) = 0?

2. Are there any methods beside the L'Hopital rule and "ln" strategic to find a limit?

Thanks a bunch pals.