$\displaystyle \text{For}\displaystyle \lim_{x \to \infty} \frac{\sin{x}}{x}=\lim_{x \to \infty} \frac{1}{x}\times \lim_{x \to \infty} \sin{x}=0 \times \text{Unknown} $

Is the answer zero?

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- Jan 3rd 2011, 08:39 AMcrossboneHow to deal with undefined limits?
$\displaystyle \text{For}\displaystyle \lim_{x \to \infty} \frac{\sin{x}}{x}=\lim_{x \to \infty} \frac{1}{x}\times \lim_{x \to \infty} \sin{x}=0 \times \text{Unknown} $

Is the answer zero? - Jan 3rd 2011, 08:47 AMArchie Meade
- Jan 3rd 2011, 09:03 AMcrossbone
Thanks! just curious, what's the answer to $\displaystyle \displaystyle \lim_{x \to \infty} sin\;x \ $? Undefined?

- Jan 3rd 2011, 09:13 AMPlato
- Jan 3rd 2011, 09:24 AMcrossbone
Thanks! btw, what are indeterminate forms as far as limits is concern?

$\displaystyle \frac{0}{0}, \frac{\infty}{\infty}, \frac{0}{\infty}, \frac{\infty}{0}, \infty \times 0$? - Jan 3rd 2011, 09:27 AMArchie Meade
- Jan 3rd 2011, 09:30 AMPlato