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Seven at One Stroke wrote:Hmm...I'm not sure if my answer is correct so check with the answer book (haven't done math in a long time).

To have a point discontinuity, then the limit of the function approaching the discontinuity needs to be the same, i.e. it cannot be asymptotic (I had to look this up on the web, sad). Since the denominator is x-a, then towards the discontinuity, there's going to be a sign shift of the value of the function as x->a. So we have to make sure that the discontinuity the function approaches to from the left and the right is a point even though the two values next to the discontinuity has opposite signs, then it makes sense that the discontinuity should be at lim(a->0)=0, which is at the x-intercepts. Then you have that at a=1,2 or 3, the funciton has a point discontinuity. (Honestly, I got the graph of the function first, and formulated my reasoning second, so there's a huge chance that this is wrong, so do think it through yourself).

I had come to the same conclusion myself, but then i actually got stuck actually determining the values of a. How did you get that?

Ranbir wrote:Yay, maths. You're using unfamiliar language to me, but no matter, america in winning in the math language department, so I guess I should get to know it. We've already accepted the american billion as being 'the billion'

I agree with Seven.
I also plotted the graph, and set a=x. It automatically set it as 0. Therefore a must be equal or greater than 1.

God I hope thats right...my credibility as a mathematician is on the line...

If x=a, wouldn't the function be undefined?
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Harimau
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Harimau wrote:I had come to the same conclusion myself, but then i actually got stuck actually determining the values of a. How did you get that?

I factored the numerator to get the three roots. I asked my friend (who's taking calculus and got him confused too). Apparently how you do these problems is simply by making the denominator a factor of the numerator, but just why that works is beyond our guesses.
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Seven at One Stroke
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Seven at One Stroke wrote:I factored the numerator to get the three roots. I asked my friend (who's taking calculus and got him confused too). Apparently how you do these problems is simply by making the denominator a factor of the numerator, but just why that works is beyond our guesses.

The answer actually came to me as i was doing a quiz today, actually.

The only reason is, if the denominator could be divided into the numerator, it would be a vertical asymptote. But if it could, then it would only be a point or removable discontinuity.

Thanks a lot though
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Harimau
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Harimau wrote:The only reason is, if the denominator could be divided into the numerator, it would be a vertical asymptote. But if it could, then it would only be a point or removable discontinuity.

Yeah, that's what my friend said. I can sort of understand why it would be a point discontinuity if we get a reduced order polynomial, but why is a function f(x)=P(x)/P'(x) have a vertical asymptote is what I'm confused about.
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Seven at One Stroke
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Seven at One Stroke wrote:Yeah, that's what my friend said. I can sort of understand why it would be a point discontinuity if we get a reduced order polynomial, but why is a function f(x)=P(x)/P'(x) have a vertical asymptote is what I'm confused about.

Well, wouldn't that just mean that P'(x) would be 0 at one point, and be a stationary point at that x-value? I think its entirely possible for a function f(x)=P(x)/P'(x) to have a vertical asymptote.
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Hey guys. I'm taking Spanish II and I'm having a tiny bit of trouble. If I put in .3% more effort, I would be doing very well. Does anyone have any tips about what I should do to study? (Except Flash Cards!!!!! )
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SesshomaruTenseiga
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SesshomaruTenseiga wrote:Hey guys. I'm taking Spanish II and I'm having a tiny bit of trouble. If I put in .3% more effort, I would be doing very well. Does anyone have any tips about what I should do to study? (Except Flash Cards!!!!! )

What level of spanish are you? If you're at intermediate or advanced, I'd get some spanish websites (like newssites) and make yourself translate them. It's excellent practice.
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SesshomaruTenseiga wrote:Hey guys. I'm taking Spanish II and I'm having a tiny bit of trouble. If I put in .3% more effort, I would be doing very well. Does anyone have any tips about what I should do to study? (Except Flash Cards!!!!!)

Depends on what you need help with. If it's mostly reading and writing, Wild_Eye's suggestion is an excellent one. If you're not that advanced yet try reading some children's books that have pictures to help you understand the words. In either case, I would recommend reading out loud: practising moving your tongue around for those words and hearing yourself say the words helps tremendously for the retention of vocabulary items, and you'll be able to tell what "sounds good" and what doesn't a lot sooner. If it's mostly listening and speaking, the best thing to do, of course, is to practise talking to a Spanish speaker. If you can't do that, try listening to Spanish songs and learn the lyrics. If you can get Spanish radio stations or TV channels, tape a few minutes of something and see if you can transcribe it (write out what they're saying).

None of those are really 0.3% effort, but if you want to improve your Spanish-learning in the long run, you should invest some time into it.
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Elven Fury wrote:Hey Yall, i think ive bitten off alot of stuff... im asking for some help... i have a project on Nuclear Chemistry and Atomic Explosions, ive looked for sites and in our book for information but have yet tot find any great information... im thinking its either going to be a speech and a comic... i know what i want to do (typical superhero thing), but, i cant find any great info and may have to change, so im coming to yall, can you help me out...?
(i also put it CA to carry on discussions about A & H bombs and what yall think about them seeing their in the news like every day being such a major threat and all...)

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