how to solve limits of trigonometric function?

how to solve these

1.limit as x approaches 0 of sin 1/x

2.limit as x approaches 0 of xsin 1/x
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1 Answer

sine (1/x) at x gotu 0....infinity

sine(x)=x -(1/3)x^3 +(1/5!)x^5+...

sine(1/x)=(1/x)-+...

as x gotu 0, 1/x gro without bound
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