Find this limit without L'Hopital's Rule

[htoor9]

Homework Statement

L'Hopital's rule does not help with this limit. Find it some other way. lim (squarert(x)/squarert(sinx)) as x -> 0+

Homework Equations

None?

The Attempt at a Solution

The only way I can think of solving this is by using L'Hopital's rule...but it obviously isn't working. How else can I find this limit?

 

[Mark44]

Homework Statement

L'Hopital's rule does not help with this limit. Find it some other way. lim (squarert(x)/squarert(sinx)) as x -> 0+

Homework Equations

None?

There are at least a couple of limits that are relevant.
$$\lim_{x \to 0} \frac{sin(x)}{x} = 1$$
$$\lim_{x \to a} f(g(x)) = f(\lim_{x \to a} g(x)), \text{provided that f is continuous at g(a)}$$

The Attempt at a Solution

The only way I can think of solving this is by using L'Hopital's rule...but it obviously isn't working. How else can I find this limit?

 

[hunt_mat]

Expand sin x as a power series...