What is the limit of this function as x approaches infinity?
2^x + x^3 / x^2 + 3^x
use an intuitive approach
the exponential expression of 2^x and 3^x become larger at a much faster rate than do x^2 and x^3
so as x --> ∞
the expression is dominated by (2^x + ?)/(? + 3^x)
--> 2^x/3^x
now as x --->∞
2^x/3^x --- 0
so limit (2^x+x^3)/(x^2 + 3^x) as x --> ∞
= 0
test it, let x = 100
expression = (1.268 x10^30) + 1000000)/(10000 + 5.154x10^47) = 2.46 x 10^-18 (close to zero)