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On May 27 2008 01:46 qet wrote:can't cancel this since its indeterminate (0/0) use L'Hopital's rule (maybe that guy who said something about the hospital was making a subtle suggestion?)
this. every time you het a fraction like 0/0 or oo/oo, just derive denominator and ... the other one, whatever it's called in english separately and see what you get. if you get 0/0 or oo/oo again, just keep deriving until you get something that makes sense.
that is in a general case, but this one is pretty trivial since it's lim[x -> 5] (1/4) = 1/4 like the other guys said.
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undefined  lol probobly wrong
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Numerator, hehe. Yes, L'Hopital...bye bye limits with 0/0 and ∞/∞. x3
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I'm assuming he is just learning calculus, so he doesn't know how to take derivatives yet, so he can't use l'hopistal's rule.
In that case, they will always factor and cancel.
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Canada7170 Posts
Fuck l'hopital. Just factor it. If you think about it, the limit --> 5 isn't equal to 5.
So it's fine to cancel.
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Fuck l'hopital. Just factor it. Bad form for later problems.
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He will learn about L'Hopital soon enough anyway 
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Canada7170 Posts
On May 27 2008 03:56 L wrote: Bad form for later problems.
Yeah but are we at later problems? Nope. If it can be factored, factor it.
The problem solving method would be:
1. Factor.
2. If it cannot be factored, use L'hopital.
the procedure is the same.
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Yeah but are we at later problems? Nope. If it can be factored, factor it.
The problem solving method would be:
1. Factor.
2. If it cannot be factored, use L'hopital.
the procedure is the same.
Or we could do
1. L'Hopital
The end.
Problems (like this one) that can be solved by inspection using factoring can be solved by inspection using L'Hopital at the same speed, honestly. Non trivial problems, by contrast, will result in time saving if you just L'Hopital them.
Ie. Bad form for later problems.
Having 1 method to cover all problems of a set reduces the amount of study time you need to cover that area and allows you to progress more quickly on tests.
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Damnit I keep messing up. Okay forget about 1/4 etc.
An example that gives 0 on the numerator and 0 on the denominator.. how would one get a limit?
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United States24753 Posts
On May 27 2008 05:45 L wrote:
Having 1 method to cover all problems of a set reduces the amount of study time you need to cover that area and allows you to progress more quickly on tests.
Depending on topic, this can be very costly. There are times when you need more than one method of solving a problem, even if you can theoretically solve it with just one method. However, I think just using L'hopital's rule for everything here is fine.
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United States5262 Posts
You look for 1/1
If you get 0/0 then use L'Hopital's.
Graphing calculators are near useless for telling you the limit.
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Judging from your previous blog posts, I think you may not have learned the L'Hopital's Rule.
1. Try to factor and cancel out the fraction before evaluating the limit. This only works in limited scenarios, mostly with polynomial quotients.
This method will not work in examples like the following:
[lim x->0] sin(x)/x
2. Use your calculator's table function. Punch in x=5.0001=(5+0.0001), and x=4.9999=(5-0.0001) [x values immediately to the right/left of the limit] in to determine the y value. If the y value converges to the same number, then it is the limit, otherwise it has no limit.
3. Use L'Hopital's Rule, which is basically evaluating the limit after differentiating both the numerator and the denominator since they are in an indeterminate form.
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Aotearoa39261 Posts
l'hospital's rule is for people who can't solve limits properly :X
factor and cancel is the cure
hell use maclaurin polynomials if you have to (in other problems)
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Im, going with Plexa on this one. No reason to use a more complicated solution if there is a simpler.
And yes, taylor (mclaurin, w/e) expansions are about 2387x more useful in limits, for example you can deduce l'hospitals rule in a line or two. Not to mention uses in big parts of the rest of mathematics, and basically all of physics.
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United States24753 Posts
Plexa and Cascade: good advice for someone going to higher math, but just blindly using L'hopital's rule isn't too bad for someone just trying to do okay in lower level calc...
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Waaaah, you people are too smart for me. Dx
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EPT![[image loading]](http://i30.tinypic.com/29c5kj5.jpg)
