SOLUTION: Okay, so I have looked for a calculus tutor online and I have a test on my homework veryy soon. I really need help. Its a La Hospital's Rule... the problem is.... lim

Algebra ->  Finite-and-infinite-sets -> SOLUTION: Okay, so I have looked for a calculus tutor online and I have a test on my homework veryy soon. I really need help. Its a La Hospital's Rule... the problem is.... lim       Log On


   



Question 170695: Okay, so I have looked for a calculus tutor online and I have a test on my homework veryy soon. I really need help. Its a La Hospital's Rule...
the problem is....
lim [ln(x)]^3/x^2
x->infinity


PLEASE help me:)

Answer by Edwin McCravy(20060) About Me  (Show Source):
You can put this solution on YOUR website!

I can't make an arrow for "approaches" easy using 
the software here, so please interpret %22%22%5Bx%2Cinfinity%5D 
as though it were xinfinity.


lim%5Bx%2Cinfinity%5D%28%28ln%28x%29%29%5E3%2Fx%5E2%29 =

We need to get that exponent 3 outside the limit.
First get it outside the parentheses:

lim%5Bx%2Cinfinity%5D%28matrix%284%2C1%2Cln%28x%29%2C%22--------%22%2C%22%22%2Cx%5E%282%2F3%29%29%29%5E3 =

Then get it outside the limit:

 =

Now with that 3 exponent outside the limit, we can use 
l'Hopital's rule on the inside without it:

 =

Multiply numerator and denominator both by 3x

 =



Edwin