Saturday, 27 September 2014

limits - Calculate limlimitsxto0+efrac1x2sinx

I want to investigate the value of lim. Since the expontial tends really fast to infinity but the sine quite slowly to 0 in comparison I believe the limit to be infinity. But I cannot find I way to prove it. I tried rewriting using the standard limit \frac{\sin x}{x} as \frac{\sin x}{x}\cdot xe^{\frac{1}{x^2}} but I still get an indeterminate form "1 \cdot 0 \cdot \infty".

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real analysis - How to find lim_{hrightarrow 0}frac{sin(ha)}{h}

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