Re: lim(x to 0) (x.sin(1/x))

In article <1122338831.116901.263610@xxxxxxxxxxxxxxxxxxxxxxxxxxxx>
"khkwa" <kiamheong@xxxxxxxxx> writes:
>Hi, I am wondering how l'Hospital rule applies in this case.
>
Firstly, put your question in the body.
Don't assume we can see the Subject: line.

lim(x to 0) (x.sin(1/x))

Secondly, list some important properties of the sin function, such as

1) sin(x) is an odd function (so sin(0) = 0)

2) It is infinitely differentiable. Its Maclaurin series converges
to the function.

3) It has period 2*pi.

4) The function and its derivatives are bounded by +-1.

5) sin(pi - x) = sin(x)

6) The many trigonometric identifies it shares with cos

7) It is the imaginary part of exp(i*x) = cos(x) + i*sin(x).

Ask yourself whether any of these (or something you list)
assists in evaluating the limit.
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