Which of the following?

Question

Which of the following functions grows at the same rate as e^x as x-->infinity?

 

a) e^2x

b) e^3x

c) e^(x+2)

d) e^-x

e) e^(-x+1)

 

Please show all your work.

Answer 1

(e^x)' = e^x → ∞

 

a) (e^(2x))' = 2e^(2x) → ∞
b) (e^(3x))' = 3e^(3x) → ∞
c) (e^(x+2))' = e^(x+2) → ∞
d) (e^(-x))' = –e^(-x) → 0
e) (e^(-x+1))' = –e^(-x+1) → 0

 

Answers are a, b, and c.

 

[See http://tutorial.math.lamar.edu/Classes/CalcI/TypesOfInfinity.aspx]

Answer 2

I am sorry, Son, do not have enough time to work on the problem right now. Just one advise:

 

take derivatives of all functions and lim for x →∝. If they are equal - they have the same rate.