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
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
$\displaystyle \displaystyle \lim_{x \to \infty}\sin{\left(\frac{x-1}{x^2 + 2}\right)} = \sin{\left[\lim_{x \to \infty}\left(\frac{x-1}{x^2 + 2}\right)\right]} = \sin{0} = 0$