General

http://imgur.com/W0onh4x

Here's the solution using L'Hopital's Rule

L'Hopital's rule just says that you can take the natural log of the limit (which allows you to pull down the exponent) under some circumstances and then set it equal to L, and e^L is the solution then. Also, it states that you can take the derivative of the numerator and the derivative of the denominator if you have a form of 0/0 once the value for x is substituted in from the limit. I used the first part between steps 1 and 2 and the second part between step 3 and 4. Then I just simplified and manipulated the limit so I could get an actual number once I substitute x in and then I just finished using the first part of L'Hopital's rule

[quote=sparkshooter]Hey, I was re-looking at the problem, and was wondering if [url=http://oi57.tinypic.com/242651d.jpg]this[/url] could also work. I'm not sure if my variable-multiplying or limit-splitting breaks any math rules.[/quote]
you're using properties of limits, which makes the solution even simpler
you have to be careful though, this only worked because the limits in the nominator and denominator exist, and because the limit of the denominator is not 0.
if, for example, the upper limit were to evaluate to infinity, then it may not have worked.

tl;dr yes, it works. good job ^^

[quote=bloodIsShed]@sparkshooter: no problem, have fun w/ your math class ^^[/quote]
Hey, I was re-looking at the problem, and was wondering if [url=http://oi57.tinypic.com/242651d.jpg]this[/url] could also work. I'm not sure if my variable-multiplying or limit-splitting breaks any math rules.

@sparkshooter: no problem, have fun w/ your math class ^^

[quote=bloodIsShed]you'd use the method suggested in the other thread.
will post a scan with solution soon

edit: [url=http://i547.photobucket.com/albums/hh471/someStriker/basil/limits_zpsed864834.jpg]suggested solution[/url][/quote]
Yeah I already knew the definition of e, I just didn't know how to change its form.
But holy cow, that was genius.
Thanks so much for the help, I get it now.

you'd use the method suggested in the other thread.
will post a scan with solution soon

edit: [url=http://i547.photobucket.com/albums/hh471/someStriker/basil/limits_zpsed864834.jpg]suggested solution[/url]

[quote=NoobCake]I'm thinking L'Hopital's Rule

Try it and lemme know what happens[/quote]
We haven't learned that, but I googled it. It sounds like it could work, but the "x" exponent makes it incredibly difficult to take the derivative.

I'm thinking L'Hopital's Rule

Try it and lemme know what happens