Need some help determining these guys:

Lim as x->infin of: ln(sqrt x) / x^2

(limit as x approaches infinity of the natural log of the square root of x all over x squared).


and

lim as x-> infin of (1+a/x)^bx


Thank you guys for your help.

lol

This post was edited by Duckling on Mar 13 2016 09:17pm

Take the derivative of the numerator and denominator:

Derivative of ln(sqrt(x)) = 1 / 2x
Derivative of x^2 = 2x

(1 / 2x) / (2x) = 1/4x

Limit as x-> infinity of 1/4x = 0


Take the ln of both sides to help get rid of the nasty raising to bx nonsense:

ln(y) = lim x -> infinity ln(1 + a/x)^bx

bx*ln(1+a/x)
ln(1 + a/x) / (1/(bx))

Derivative of ln(1 + a/x) = (1 / ( 1+a/x)) * ( -a/x^2)
Derivative of 1/(bx) = -1/(bx^2)

Starting to get messy so I don't want to finish, but just continue to simplify algebraically that first derivative divided by the second one and it should come out easily.

This post was edited by RzChaos on Mar 13 2016 09:29pm

Yeah no worries, I just suck at getting these things started. Thanks again man, really appreciate it.

Whoops: In the first question, (1 / 2x) / (2x) = 1/4x^2, not 1/4x, but the final answer is still zero.

can help if you have anymore questions