Question #81fbb

1 Answer
Dec 23, 2017

Lim_(xrarroo)(ln(x+e^x))/x=1

Explanation:

Lim_(xrarroo)(ln(x+e^x))/x=oo/oo

Using L'Hopitals rule:

Lim_(xrarroo)(1/(x+e^x)*(1+e^x))/1

Lim_(xrarroo)(1+e^x)/(x+e^x)=oo/oo

Again

Lim_(xrarroo)(e^x)/(1+e^x)=Lim_(xrarroo)cancel(e^x)/(cancel(e^x)(1/(e^x)+1))

=Lim_(xrarroo)1/(1/(e^x)+1)=1/(1/oo+1)=1/(0+1)=1