Question

Hi, I need some help with L'Hospital with this exercise: lim->inf [ln (x) / sqrt (x)]

Answer 1

I know that if I try to resolve it, it gives me inf/inf that is a indeterminate form so what I did was that I derivate ln(x) and sqrt(x)

Answer 2

\[((1/x)/(1/2\sqrt{x}))\] this is mi Hospital derivative

Answer 3

Basically for L'hospital's rule you take the derivative of the function until it doesn't an indeterminate form. When you do that for this you (1/x)/(1/2sqrt(x)) = 2sqrt(x)/x and then I think you're done I'm not sure how far you have to go with an infinite limit.

Answer 4

i have that but if I resolve that substituting the x with inf it gives me something like 2sqrt(inf)/inf = inf/inf and that's an indeterminate form also

Answer 5

the result is 0, I resolve it but thanks anyway!

Answer 6

sorry I couldn't help more

Answer 7

after you use L'Hospitals rule... simplify...then take the limit.

Answer 8

\[(2\sqrt{x})/x\]