Find the limit of this calculus problem.?

Question

(5x-3)/(ln(5+4e^(x))

x=inf

Answer 1

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

Answer 2

5x+2xa-6ab