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| EV33 |
 Posted: Mon Apr 21, 2008 8:28 pm Post subject: Limit problem |
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Forum Freshman
Joined: 04 Nov 2007
Posts: 52
Location: Washington State
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We are reviewing limits again and Im lost on this problem. Could someone walk me through it...
(x-5)(x^(2)-25)^(-.5)
When I find the derivative of the bottom am I supposed to look at it as if it were to the negative one half or positive one half? That is really my main confusion. |
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| Chemboy |
| Posted: Mon Apr 21, 2008 9:09 pm Post subject: |
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Joined: 01 Jul 2006
Posts: 959
Location: NY
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Just to clarify... is the function (x-5)/sqrt(x2-25)? And if this is a limit problem as in
"lim x-->something of something," it would help to see the actual limit portion of it...
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"There is a kind of lazy pleasure in useless and out-of-the-way erudition." -Jorge Luis Borges |
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| EV33 |
| Posted: Mon Apr 21, 2008 9:18 pm Post subject: |
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Location: Washington State
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| Yes you are correct. And it is the limit as x approaches 5 |
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| Chemboy |
| Posted: Mon Apr 21, 2008 9:40 pm Post subject: |
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Ok, so lim x-->5 (x-5)/sqrt(x2-25) equals, as I'm sure you've realized, 0/0, which is an indeterminate form. So, as you seem to realize, you need to use L'Hopital's rule from here. When you use L'Hopital's rule, you take the derivatives of the top and bottom separately (so you won't be using the quotient rule). With that, I think you should have an answer to your question about the square root...
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| serpicojr |
| Posted: Mon Apr 21, 2008 9:42 pm Post subject: |
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| The important point that Chemboy makes is that, to apply l'Hopital's rule, you need to be looking at a ratio of functions. You need a function on top and a function on bottom. The original way you wrote this did not display this fact, so on the surface it wouldn't even make sense to apply l'Hopital's rule. |
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| EV33 |
| Posted: Mon Apr 21, 2008 9:47 pm Post subject: |
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Location: Washington State
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| So then would I write the first derivative as 1/1/4xsqrt(x2-25) which would just be 4xsqrt(x2-25)? |
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| serpicojr |
| Posted: Mon Apr 21, 2008 10:32 pm Post subject: |
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| Check that bottom derivative again. |
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| JaneBennet |
| Posted: Tue Apr 22, 2008 2:48 am Post subject: |
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Joined: 06 Apr 2008
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You do not need L’Hôpital’s rule here. Observe that
Hence
Note that the limit has to approach from the right as the function is not defined for −5 < x < 5.
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| thyristor |
| Posted: Tue Apr 22, 2008 5:59 am Post subject: |
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| JaneBennet wrote: |
You do not need L’Hôpital’s rule here. Observe that
Hence
Note that the limit has to approach from the right as the function is not defined for −5 < x < 5. |
JaneBennet, how do you write that in your post? (the sqrt and division)
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373 13213-mbm-13213 373 |
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| JaneBennet |
| Posted: Tue Apr 22, 2008 6:27 am Post subject: |
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Joined: 06 Apr 2008
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Well, I formatted the equations using LaTeX on a math site that has LaTeX installed, then I saved and uploaded the GIF images. 
There are plenty of math sites on which you can type equations in LaTeX – http://www.mathisfunforum.com/index.php was where I did the above samples. 
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| thyristor |
| Posted: Tue Apr 22, 2008 9:29 am Post subject: |
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Ok, thanks 
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