Which of the following functions grows the slowest as x goes to infinity?

Question

Which of the following functions grows the slowest as x goes to infinity?

A	xe
B	ex
C	ex
D	They all grow at the same rate.

Answer 1

It's easiest to see if you plot all three.

Answer C is just a line with a slope of e, so it grows slower than the other two functions with grow exponentially.

Answer 2

Well here's a table courtesy of MS Excel...

Which one looks like it grows the slowest as x goes to infinity ????

x e^x x^e e*x

100 2.68812E+43 273252.1935 271.8281828

250 3.7465E+108 3298198.207 679.5704571

500 1.4036E+217 21705066.38 1359.140914

600 3.773E+260 35628542.84 1630.969097

700 1.0142E+304 54172428.16 1902.79728

709.5 1.355E+308 56194278.84 1928.620957

710 #NUM! 56301991.59 1929.980098

Note that y=e*x is a line with slope e

y=x^e is something like x^(2+h) where h is a decimal number