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Hi! I've been meaning to ask, and I think that this board is more related than /wsr/ for this. Anyway. I've been doing my math homework, and I was wondering on how to go about it. I've looked at some tutorials online, but now my problem is that, it seems that almost every example that they give me, they use some trick to solve it.
I know this sounds vague, so allow me to give an example. If i were to solve a function limit question: (lim, t-1) t^3-t/t^2-1. I get that in order to use that specific equation, i need to factorize it, so i'll have: t(t^2-1)/(t^2-1), and you go about solving the thing.
But my problem is with this, how can you know exactly how to manipulate the equation in order to solve the equation, like the guy who was explaining the above equation, knew that he had to use factorization in order to solve the equation, but how? Or when do I need to rationalize a fraction in order to get the right answer? Am I missing the point of math entirely?
I'm sorry if this might be considered inappropriate for the board, I just feel like the fact of not knowing what to do or where to start, gives me more frustration and headaches, and I need help. PLEASE.
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I guess basically what I'm asking is, how do I get math?
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I think you need to practice your algebra
factoring polynomials allows you to substitute a limit so that the denominator doesn't result to zero (can't divide by zero). doing that enables you to find where the limit exists
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>>8729386
I know that, but how do I know which method to use when? Are you saying that it will come naturally as I just plow through different worksheets?
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>>8729390
The general idea for solving indeterminate limits of any kind is to split them into several parts. For polynomials factorization is probably the sanest of ways to achieve this.
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>>8729402
sure, and I might sound really stupid, but how do you know what parts to split them into? is there some kind of rule? Also sometimes, people split these into very counter-intuitive parts, so to me it doesn't make any sense until the end
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>>8729411
Partial fraction decomposition is a straight-forward procedure, and it guarantees the resulting parts are not indeterminate, so there shouldn't be really any problems with limits of polynomial fractions. In the general case you can only rely on experience and practice, I think.
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>>8729451
thanks, I'll try doing just that. Also wow quite big words there you're throwing around.
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