Problem Limit 4_2

**gilyos** · December 22nd 2009, 10:32 AM

$lim_{x \to 0+} \frac{xsin^2\frac{1}{x}}{sin^2\frac{1}{x}+cos^2\fr ac{2}{x}}$

$lim_{x \to 0-} \frac{xsin^2\frac{1}{x}}{sin^2\frac{1}{x}+cos^2\fr ac{2}{x}}$

**tonio** · December 22nd 2009, 11:23 AM

Originally Posted by gilyos

$lim_{x \to 0+} \frac{xsin^2\frac{1}{x}}{sin^2\frac{1}{x}+cos^2\fr ac{2}{x}}$

$lim_{x \to 0-} \frac{xsin^2\frac{1}{x}}{sin^2\frac{1}{x}+cos^2\fr ac{2}{x}}$

$\left|\frac{x\sin^2\frac{1}{x}}{\sin^2\frac{1}{x}+ \cos^2\frac{2}{x}}\right|\le \left|\frac{x\sin^2\frac{1}{x}}{\sin^2\frac{1}{x}} \right|=|x|\xrightarrow [x\to 0]{}0$

Tonio

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