Question

How do you find the Limit of `(lnx)^3/x^2` as x approaches infinity?

Answer 1

`lim_(xto+oo)(lnx)^3/x^2=0`

Explanation:

`lim_(xto+oo)(lnx)^3/x^2=_(DLH)^(((+oo)/(+oo)))`

`lim_(xto+oo)((3(lnx)^2)/x)/(2x)=`

`lim_(xto+oo)(3(lnx)^2)/(2x^2)=`

`3/2lim_(xto+oo)(lnx/x)^2=0`

because

• `lim_(xto+oo)lnx/x=_(DLH)^(((+oo)/(+oo)))`

`lim_(xto+oo)1/x=^((1/(+oo)))=0`