How to solve the following question without using the l'hospital rule?

lim_(x to oo) ln(e^x+3x)/x^3

1 Answer
Aug 10, 2018

lim_(xto oo) ln(e^x+3x)/x^3=0

Explanation:

lim_(xto oo) ln(e^x+3x)/x^3

e^x+3x~=_(oo)e^x, because

lim_(x to oo)(e^x+3x)/e^x=1+(3x)/e^x=1

so : lim_(xto oo) ln(e^x+3x)/x^3

=lim_(xtooo)ln(e^x)/x^3

lim_(x to oo)=1/x^2

=0

\0/ Here's our answer !