Help me find the limit of this function?

Question

lim sqrt(x)/sqrt(sin x)
x->0+

I tried l'hopital rule, but couldn't get it to work. I am a little rusty on this so i'd appreciate some help.
thanks

Answer 1

Lim sqrt(x / sin x) = sqrt (Lim (x /sin x)) = sqrt (1) = 1

Answer 2

f(x) = √x
g(x) = √(sin(x))
so the function is
f(x)/g(x) = (√x)/(√sin(x)) = √(x/sin(x)). Now,
x/sin(x) (by L'Hopital's rule) becomes
1/cos(x) and so becomes 1 as x ->0 so that
lim x -> 0 (√x)/(√(sin(x)) = 1

Hope that helps ☺


Doug