Which of the following functions grow faster then e^x as x approaches infinity?

x^4

ln(x)

e^(-x)

3^x

.5*e^x

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- Mar 12th 2008, 07:22 PMDINOCALC09which grows fastest?
Which of the following functions grow faster then e^x as x approaches infinity?

x^4

ln(x)

e^(-x)

3^x

.5*e^x - Mar 12th 2008, 07:38 PMThePerfectHacker
3^x because it is e^(xln 3) while e^x is just e^(x*1) and ln 3 > 1.

- Mar 13th 2008, 05:08 AMcolby2152
Another reason as to why...

$\displaystyle 3^x > e^x$

Same exponent, but the left side has a larger base hence a larger outcome, and to connect this to TPH's explanation..

$\displaystyle ln|3|x > x$

$\displaystyle x \ne 0$ <- this follows because at zero the functions are equal

$\displaystyle ln|3| > 1$