Find the right end behaviour of x^3- e^(-x).
The answer choices are -x^3, x^3, -e^-x, e^-x, e^x.
without graphing .....
"right end behaviour" to me means x ---> +∞
let's look at a somewhat large number
e.g.
x = 100
our expression is 100^3 - 1/e^100
my calculator says:
1000000 - 3.7 x 10^-44
= appr 1000000 wouldn't you say ?
that is, as x gets larger, the -e^(-x) becomes infinitely small or practically zero
so just by getting a "feel" for the numbers , the obvious choice is x^3