gabpin
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theBMB
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for the first one, looks like multiplying by root t -2 on top and bottom doesn't fix it. You may want to try squeeze theorem. There might be a technique i'm forgetting right now
for the second one, plug x-1 into the equation for x, then evaluate and pull out a factor of (x-1), with that in mind, part b should be simple
don't really feel like reading the 3rd problem
for the second one, plug x-1 into the equation for x, then evaluate and pull out a factor of (x-1), with that in mind, part b should be simple
don't really feel like reading the 3rd problem
theBMB
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:/
well basically, the idea is that you use two well known limits to solve the problem. The two limits you use must have the same limit. The first limit should be lower than the given equation for all values of x. The second limit should be greater than the given equation for all values of x. Since both of these known limits converge to the same point and the given equation is inbetween these two limits, the given equation is "squeezed" to the same limit.
TBH I'm not completely sure that theorem applies in this case since the limit does not go to infinity. I'd have to look it up, but when L'hopital is ruled out, squeeze theorem is the next best bet beyond simply manipulating the equation into a more manageable form.
well basically, the idea is that you use two well known limits to solve the problem. The two limits you use must have the same limit. The first limit should be lower than the given equation for all values of x. The second limit should be greater than the given equation for all values of x. Since both of these known limits converge to the same point and the given equation is inbetween these two limits, the given equation is "squeezed" to the same limit.
TBH I'm not completely sure that theorem applies in this case since the limit does not go to infinity. I'd have to look it up, but when L'hopital is ruled out, squeeze theorem is the next best bet beyond simply manipulating the equation into a more manageable form.
theBMB
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transform it into what? a more manageable form?
you have to use basic algebraic techniques, factoring, multiplying the denominator on top and bottom, completing the square, multiplying by the inverse, etc. There's always some trick to it that's fairly straightforward once you figure it out, but figuring it out is usually the tough part.
as for the 3rd problem, it's a related rates question. Look up a formula in your textbook about concentration. In all likelihood there's an example in your book that will tell you exactly how to do it. (I don't remember the exact concentration formula atm)
you have to use basic algebraic techniques, factoring, multiplying the denominator on top and bottom, completing the square, multiplying by the inverse, etc. There's always some trick to it that's fairly straightforward once you figure it out, but figuring it out is usually the tough part.
as for the 3rd problem, it's a related rates question. Look up a formula in your textbook about concentration. In all likelihood there's an example in your book that will tell you exactly how to do it. (I don't remember the exact concentration formula atm)
theBMB
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one thing that might make it easier is that you can factor out the 3 and basically ignore it so you get 3(t^3-64)/(root(t)-2)
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