Calculus/proving

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Expert: - 4/29/2009


Question
So how do I prove this:

Find the limit     lim        Sinx
             x-> Infinity   -------
                               x

I have to state which theorems are used and definitions I used to prove this statement. Any help??

Answer
Question:  
So how do I prove this:

Find the limit     lim        Sinx
            x-> Infinity   -------
                              x

We know that |sin(x)|<=1.  The lim(x->∞)1/x = 0,
so we know this is smaller, therefore it goes to 0 also.




If this were lim(x->0) of the same problem,
the Taylor's series for sinx would be used.
sinx = x - x^3/3! + x^5/5! - x^7/7! ...
When this series is divided by x, the first term is 1.
The rest all go to 0, so the answer is 1.  

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