i have the equation:

so i get this

when i check the answer i have this :

i do not know how to go from what i have to the answer.

for some reason √ doesnt like it in math wrap.

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- March 6th 2011, 05:25 PMDAngelsolving a fonction problem
i have the equation:

so i get this

when i check the answer i have this :

i do not know how to go from what i have to the answer.

for some reason √ doesnt like it in math wrap. - March 6th 2011, 05:30 PMtopsquark
- March 6th 2011, 11:09 PMDAngel
can you show me. im not sure what you mean. i dont understand how he goes from what i ahve to the answer. what i mean is the logic behind it.

- March 7th 2011, 02:44 AMHallsofIvy
Do what topsquark said! What do you get when you multiply

? - March 7th 2011, 10:48 AMtopsquark
I've never taken a course in Analysis, but my take on why we rationalize the numberator is simply that the trick works. Now that you've seen what to do with this problem you know that you can do it to others similar to it.

(Eventually you'll take the limit of your answer as h goes to 0. Then you'll see why this simplifies the problem rather than make it more difficult.)

-Dan - March 7th 2011, 12:20 PMDAngel
i must not see what you mean. i tried, all i end up is with the same equation since they just cancel each other out.

would you mind showing me the steps you used to make solve the problem? - March 7th 2011, 12:28 PMtopsquark
- March 7th 2011, 12:32 PMTheChaz
They only cancel each other out IF YOU CANCEL THEM! That might sound funny, but the point of us inserting the same factor on top and on bottom is to somehow combine/rearrange so that we get something ELSE to cancel...

"FOIL" out the top. You will have "h" remaining. Just h. This cancels with the h factor on bottom.

Then directly substituting h = 0 will give something meaningful, and the answer. - March 7th 2011, 01:32 PMDAngel
yes it does help. but for some reason i dont see how to do the rest.

if i have

im still stuck because i dont see how to go beyond that.

TheChaz, im unsure what you are trying to say. - March 7th 2011, 02:04 PMTheChaz
- March 7th 2011, 06:31 PMDAngel
completly forgot about this

then once i do the rest i end up with h on top and bottom and cancel them out. thanks for the help - March 7th 2011, 06:36 PMTheEmptySet
just FYI if you use (\sqrt{a})^2=a you will get