Hi
So I am applying l'Hospital's Rule to
lim (9x)/(ln (3x + e^x))
x-> infinity
What I wondering is ln (3x + e^x) = ln 3x + ln e^x and then do they both just become 1/3x and 1/e^x?
Any insight would be appreciated
Thanks
Still a calculus beginner
So lim 9x/ ln (3x + e^x) becomes 9/ (3 + e^x)/(3x + e^x)
x->infinity
which becomes (27x + 9e^x)/(3 + e^x) which is again infinity/infinity
so I am thinking I need to apply the l'Hospital's rule again
so now I apply the quotient rule so it becomes
((27 + 9e^x)(e^x) - (e^x)(27x + 9e^x))/((e^x)^2)
so (27 + 9e^x - 27x-9e^x)/e^x = (27 - 27x)/e^x so I still have infinity/infinity
where am I going wrong????
Thanks
Calculus Beginner
Sorry I am now confusing myself
Am I right.... applying l'Hospital's rule a second time I get
lim (27x + 9e^x)/ (3+ e^x) = lim 27 + 9e^x/e^x
x-> infinity
so then I apply l'hospital's rule a third time to get
lim 9e^x/e^x = 9
x-> infinity
Am I right???
Thanks
Calculus Beginner