Which of the following functions grows the fastest as x grows without bound?

Question

Which of the following functions grows the fastest as x grows without bound?

 f(x) = e^x 

g(x) = e^cosx 

h(x) =  

They all grow at the same rate.

Answer 1

e is approximately 2.718.

5/2 = 2.5

therefore e^x increases more quickly than (5/2)^x as x goes to ∞

e^{cos x} oscillates between e and 1/e, i.e. it does not increase.