# Relative Rates of Growth

• Mar 18th 2010, 02:52 PM
AIYAH
Relative Rates of Growth
Order the function from slowest-growing to fastest growing as x--> infinity. Show your work.

x^(6), e^(x), 6^(x), (ln(6))^(x)

I don't know how I would go about comparing 4 functions together.. also i'm having trouble evaluating

e^x to 6^x.. i keep getting an indeterminate form..
• Mar 18th 2010, 02:56 PM
pickslides
Quote:

Originally Posted by AIYAH

e^x to 6^x.. i keep getting an indeterminate form..

Can't you say as

$\displaystyle 6 > e$ then as $\displaystyle x\to\infty, 6^x > e^x$
• Mar 18th 2010, 03:35 PM
AIYAH
Quote:

Originally Posted by pickslides
Can't you say as

$\displaystyle 6 > e$ then as $\displaystyle x\to\infty, 6^x > e^x$

Oh yes that is true.. now the next part of the question... hmm.
• Mar 18th 2010, 03:45 PM
pickslides
The next part? I'm not sure exactly what you mean?

$\displaystyle 6 > e > \ln(6)$ then as $\displaystyle x\to\infty, 6^x > e^x > \ln(6)^x$
• Mar 18th 2010, 03:50 PM
AIYAH
ohhh.. i can do that to the other problems too.
i get it now ^.^