Evaluate the limit Calculus

Question

((4+8(4^x)) / ((9-2(4^x)) as x approaches infinity

Answer 1

Intuitively, can you see that as "x" gets VERY large, the constant "4" on the top and the constant "9" on the bottom become extremely insignificant (they are completely overshadowed by the "8(4^x)" and the -2(4^x) which means the result is 8(4^x)/-2(4^x) and the "4^x" cancels giving you 8/-2 which is -4?

If you insist that you need an algebraic way to determine the limit, then here is one:

At this point, you say that the limit as x→∞ of 4/4^x = 0 and the limit of 9/4^x is also zero, and the 4^x cancels out so you end up with 8/(-2) = -4.