Hi community!

Just introducing myself as per recommendation after the registration process. Nice to meet you all.

I'm doing a homework problem that is stated: "Suppose that a is a positive constant and that R is the region bounded above by y = 1/x^{a}, below by y = 0 and on the left by the line x = 1. Part A asks to sketch the graphs for a = .5, 1 , and 2 and then asks which is closest to the x axis.

Computationally, I know the answer is 1/x^{2 }but isthere any other way to prove that that function approaches the x axis faster than the other two functions?I attempted the limits for each function and naturally they all approach 0 when x -> infinity.

Thanks again,

Alta