Hello,

I am having trouble finding the following limit:

lim as x -> infinity of sin(x-1/x^2+2)

Factoring the denominator does not help.

Please help?

Thanks so much :)

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- Feb 19th 2011, 07:08 PMtigerlilyNeed help with limit
Hello,

I am having trouble finding the following limit:

lim as x -> infinity of sin(x-1/x^2+2)

Factoring the denominator does not help.

Please help?

Thanks so much :) - Feb 19th 2011, 07:36 PMmr fantastic
- Feb 19th 2011, 07:54 PMProve It
I don't see how this helps, considering $\displaystyle \displaystyle \frac{x-1}{x^2 - 1} \neq \frac{x - 1}{x^2 + 2}$...

Instead, $\displaystyle \displaystyle \lim_{x \to \infty}\frac{x - 1}{x^2 + 2} = \lim_{x \to \infty}\frac{\frac{1}{x} - \frac{1}{x^2}}{1 + \frac{2}{x^2}} = 0$.

And from the continuity of the sine function

$\displaystyle \displaystyle \lim_{x \to \infty}\sin{\left(\frac{x-1}{x^2 + 2}\right)} = \sin{\left[\lim_{x \to \infty}\left(\frac{x-1}{x^2 + 2}\right)\right]} = \sin{0} = 0$ - Feb 19th 2011, 08:37 PMmr fantastic