EPTlim x-5
(x-5)/(4x-20)
(5-5)/(20-20)
produces 0/0
What is the limit?
0/0, so do we use a graphing calculator to determine the limit?
Limits that gives 0/0
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Raithed
China7078 Posts
lim x-5 (x-5)/(4x-20) (5-5)/(20-20) produces 0/0 What is the limit? 0/0, so do we use a graphing calculator to determine the limit? | ||
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Boblion
France8043 Posts
edit: u mean limit @ 0 ? or +oo ? +oo ---> 1/4 edit2: i suck | ||
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Boblion
France8043 Posts
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Raithed
China7078 Posts
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Boblion
France8043 Posts
(x-5)/(4x-20) = (x-5)/(4*(x-5)) = 1/4 ? | ||
Jibba
United States22883 Posts
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Boblion
France8043 Posts
On May 26 2008 23:48 Jibba wrote: THIS QUESTION IS SO TOUGH YOU MIGHT HAVE AN ANXIETY ATTACK AND NEED TO GO TO THE HOSPITAL CAN YOU SIR TELL ME IF MY ANSWER IS RIGHT ??? IT LOOKS TOO EASY TO BE TRUE 1!!11!!! | ||
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Jibba
United States22883 Posts
On May 26 2008 23:51 Boblion wrote: CAN YOU SIR TELL ME IF MY ANSWER IS RIGHT ??? IT LOOKS TOO EASY TO BE TRUE 1!!11!!! It's not. Come on, you're French you should know this. EDIT: Oh wait, your second post is but I don't think that's they way they want it to be done. | ||
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Ecael
United States6703 Posts
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Boblion
France8043 Posts
On May 26 2008 23:54 Jibba wrote: It's not. Come on, you're French you should know this.  Hahah i did a mistake in my first post. lololol what a nub i'm. | ||
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arbiter_md
Moldova1219 Posts
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kekekekyle
Canada32 Posts
lim (x-5)/(4x-20) =1/4 | ||
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azndsh
United States4447 Posts
On May 26 2008 23:48 Jibba wrote: THIS QUESTION IS SO TOUGH YOU MIGHT HAVE AN ANXIETY ATTACK AND NEED TO GO TO THE HOSPITAL THE HOSPITAL MIGHT GIVE YOU A RULE ABOUT SOLVING THESE QUESTIONS OMG | ||
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Jibba
United States22883 Posts
I'll give you a hint. The French guy didn't actually come up with it. | ||
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Jibba
United States22883 Posts
On May 27 2008 00:02 azndsh wrote: THE HOSPITAL MIGHT GIVE YOU A RULE ABOUT SOLVING THESE QUESTIONS OMG L' | ||
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Boblion
France8043 Posts
 i made a correction. | ||
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mikeymoo
Canada7170 Posts
Presto. | ||
Chill
Calgary25991 Posts
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qet
Australia245 Posts
use L'Hopital's rule (maybe that guy who said something about the hospital was making a subtle suggestion?) ![[image loading]](http://i30.tinypic.com/29c5kj5.jpg) | ||
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Boblion
France8043 Posts
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GeneralCash
Croatia346 Posts
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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spec. opps
United States127 Posts
 lol probobly wrong | ||
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Descent
1244 Posts
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Seraphim
United States4467 Posts
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fight_or_flight
United States3988 Posts
In that case, they will always factor and cancel. | ||
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mikeymoo
Canada7170 Posts
So it's fine to cancel. | ||
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L
Canada4732 Posts
Fuck l'hopital. Just factor it. Bad form for later problems. | ||
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Naib
Hungary4844 Posts
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mikeymoo
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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L
Canada4732 Posts
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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Tynuji
127 Posts
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Raithed
China7078 Posts
An example that gives 0 on the numerator and 0 on the denominator.. how would one get a limit? | ||
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fight_or_flight
United States3988 Posts
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micronesia
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. | ||
jkillashark
United States5262 Posts
If you get 0/0 then use L'Hopital's. Graphing calculators are near useless for telling you the limit. | ||
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KH1031
United States862 Posts
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. | ||
Plexa
Aotearoa39261 Posts
factor and cancel is the cure hell use maclaurin polynomials if you have to (in other problems) | ||
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Cascade
Australia5405 Posts
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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micronesia
United States24753 Posts
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Raithed
China7078 Posts
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fight_or_flight
United States3988 Posts
On May 27 2008 10:37 Raithed wrote: Waaaah, you people are too smart for me. Dx how about you give us an example that can't be done with factoring | ||
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qet
Australia245 Posts
On May 27 2008 12:12 fight_or_flight wrote: how about you give us an example that can't be done with factoring try: lim sin(x) / x .... x->0 can't be done with factoring | ||
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tiffany
3664 Posts
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wanderer
United States641 Posts
i didnt see anyone tell the story about it though so here goes: once upon a time, there were two brothers. they were called the Bernoulli Brothers. you've probably heard of them in science class for the Bernoulli Effect. well something you don't learn in class goes like this: one day a rich aristocrat named L'Hospital was riding on the bandwagon as new discoveries in mathematics were being revealed. he knew that the people who discovered these things would be remembered for a long, long time; so he wanted in on it. when one of the Bernoulli brothers (i forget which one) discovered this rule, he was given a bunch of money by monsieur L'Hospital to name the rule after him, thus saving his name to posterity. Besides, there was already a Bernoulli Principle, so why not? [/story] lim x->5 [ x-5 / 4x-20 ] => d [ x-5 ] / dx = 1 d [ 4x-20 ] / dx = 4 (this is L'Hospital's rule in action) => lim x->5 [ 1 / 4 ] = 1/4 Important note: you CAN NOT do this whenever you want. you can only do this when the limit, as it is worded, goes to 0/0 or (+/- oo) / (+/- oo). the bernoulli brothers had no idea why this was true and couldn't prove it -- it just worked. weird coincidence. thats why its called "L'Hospital's Rule" instead of "L'Hospital's Theorem/Law". [/history + math help] HOW TO DO ANY L'HOSPITAL'S RULE PROBLEM: courtesy of qet, although the name isn't spelled correctly. | ||
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qet
Australia245 Posts
On May 27 2008 16:48 wanderer wrote: courtesy of qet, although the name isn't spelled correctly. according to wikipedia: http://en.wikipedia.org/wiki/L'Hôpital's_rule can be spelt either "l'Hôpital" or "l'Hospital" but i was taught no 's'. | ||
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jgad
Canada899 Posts
On May 27 2008 07:29 micronesia wrote: 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. I agree. I teach at university level and one of the most important things, I feel, to get across to students is the ability to look at a problem from more than one angle. The idea that one can just store a rule like L'Hopital's and use it on a certain type of problem is the sort of thing that gets people stuck. In the worst case I find it produces the sort of people who understand that the rule will solve a certain type of problem but who don't understand the mechanism you would use to solve the problem without the rule or understand the limitations on the rule with respect to when it is or isn't applicable. I think the best rule is to only use higher-level methods to solve a problem when you already understand the "hard way" to the solution but simply need the answer - say as a step in an engineering application or in solving a more difficult set of equations. If this question is being asked from the context of a course which is teaching more fundamentals methods in mathematics, then while the L'Hopital's solution may be keen (and may even impress the teacher), it may be missing the more simplistic algebraic solution to the problem and teaching bad habits early. Just a thought. | ||
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sigma_x
Australia285 Posts
The present question, however, is much easier than that because division by a common factor will yield the answer immediately. Edit: There are other methods of course, the most well known being the squeeze theorem. Other more advanced methods require knowledge of set topology. | ||
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