When working with a limit of e^x such as:

The limit as x approaches infinity of

Can I simply state that it tends towards 1/((e^inf)/inf) and therefore to 0, or is the limit not yet defined since it tends towards inf/inf below 1? Thanks.

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- October 12th 2013, 07:03 AMPazeLimit of e^x
When working with a limit of e^x such as:

The limit as x approaches infinity of

Can I simply state that it tends towards 1/((e^inf)/inf) and therefore to 0, or is the limit not yet defined since it tends towards inf/inf below 1? Thanks. - October 12th 2013, 07:50 AMemakarovRe: Limit of e^x
Why do you think that 1/((e^inf)/inf) is 0? In general, you can't compare infinities.

- October 12th 2013, 11:39 AMPazeRe: Limit of e^x
- October 12th 2013, 11:49 AMemakarovRe: Limit of e^x
Yes, you could use L'Hopital's rule. To find limits, you need some database of standard facts, e.g., as provided and . The fact that the where is one of those standard facts, but one has to prove it for the first time.

- October 12th 2013, 03:05 PMHallsofIvyRe: Limit of e^x
You could also use the MacLaurin series for , so that .

Now you have .

Divide both numerator and denominator by to get which goes to infinity as x goes to infinity. Notice that, by this argument, . - October 12th 2013, 03:47 PMPazeRe: Limit of e^x
- October 12th 2013, 03:52 PMPlatoRe: Limit of e^x
- October 12th 2013, 06:08 PMPazeRe: Limit of e^x