calculus
posted by Zel on .
Find the limit of this calculus problem.?
(5x3)/(ln(5+4e^(x))
x=inf

Intuitive approach
for large values of x, the 5 of (5 + e^x) becomes insignificant , so for all practical purposes
we just have to look at ln(4e^x)
which is ln4 + lne^x
= ln4 + x
Also for very large values of x, the constant ln4 is relatively insignificant, so the denominator
approaches x for large values of x
Now look at the top.
Again for large values of x , the 3 becomes meanignless compared to the size of 5x
So for large values of x
our expression becomes
lim 5x/x as x > infinity
= 5 
5x+2xa6ab