1. ## finding the limit

what is the limit limit as x-> infinity of
(sin x) / sqrt(x)

i know lim (sin x)/x = 1
but how do i find the one above???

2. Hello,
Originally Posted by razorfever
what is the limit limit as x-> infinity of
(sin x) / sqrt(x)

i know lim (sin x)/x = 1
but how do i find the one above???
Note that for a positive x, $\displaystyle x=\sqrt{x} \sqrt{x}$

hence $\displaystyle \sqrt{x}=\frac{x}{\sqrt{x}}$

your limit is thus $\displaystyle \frac{\sin(x)}{x} \cdot \sqrt{x}$

3. Originally Posted by razorfever
what is the limit limit as x-> infinity of
(sin x) / sqrt(x)

i know lim (sin x)/x = 1
but how do i find the one above???
I hope you don't know that! sin(x)/x goes to 1 as x goes to 0 but your limit is for x going to infinity. You know that sin(x) is never larger than 1 nor less than -1: $\displaystyle \frac{-1}{x}\le\frac{sin x}{x}\le\frac{1}{x}$. Now, what happens to those end terms as x goes to infinity?

Moo's hint would be relevant if the limit were as x goes to 0. I think you mislead him!