Question

How do you use L'hospital's rule to find the limit `lim_(x->oo)ln(x)/sqrt(x)` ?

Answer 1

By l'Hopital's Rule,
`lim_{x to infty}{lnx}/sqrt{x}=0`.

Let us look at this limit in more details.
By l'Hopital's Rule,
`lim_{x to infty}{lnx}/sqrt{x} =lim_{x to infty}{1/x}/{1/{2sqrt{x}}}`
by multiplying the numerator and the denominator by `2sqrt{x}`,
`=lim_{x to infty}{2sqrt{x}}/{x}=lim_{x to infty}2/sqrt{x}=0`