Recent content by iatnogpitw

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    Solving a Tricky Integral Homework Problem

    Homework Statement Okay, here's the problem: integrate ((x^3) - 1) / ((x^3) + x) dx Homework Equations What is the solution and the method? The Attempt at a Solution I know this involves partial fractions, which I attempted to no avail, since the numerator is the same degree as the...
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    Integrating {(x^2) / sqrt[(x^2) - 9] } dx

    Tricky Integral?? Homework Statement So the problem is to integrate this: {(x^2) / sqrt[(x^2) - 9] } dx I cannot, for the life of me, solve this problem, and I know it's not that hard. I have tried using trig substitutions x = 3 cos(theta) and x = 3 sec(theta) but for some reason, maybe a...
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    An oddly puzzling differential equation

    Homework Statement Solve t*y'(t) + 4*y = 0; y(3) = 2. This is the solution---> Ans: y(t) = 162t^(-4)Homework Equations I need to know how my professor got this answer.The Attempt at a Solution I attempted by subtracting 4y to the other side and separated the variables to yield...
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    What is the limit of tan(x)^sin(x) as x->0+

    Okay, so I got ((1/(tan(x)(cos^{2}(x))))/((sin(x))/(cos^{2}(x)) = (cos(x)/(sin^{2}(x)) This limit still equals infinity though, and I can' see L'hopital's rule getting me any beyond a term with infinity in it. EDIT: Oh, so does that mean the limit DNE?
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    What is the limit of tan(x)^sin(x) as x->0+

    What is the limit of tan(x)^sin(x) as x-->0+ Homework Statement Lim\rightarrow0^{+}((tan(x))^{sin(x)}Homework Equations I know that you have to raise e to this limit and you can then bring down sin(x) to get (sin(x))(ln(tan(x))), but beyond that, I am stuck.The Attempt at a Solution I guess...
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    Convergent or Divegent Series?

    Right, I forgot about the partial sums. Thanks, that helped a lot. But isn't 1/(\sqrt{k+2}) smaller than (ln(k))/(\sqrt{k+2})?
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    Convergent or Divegent Series?

    Homework Statement \sum{(ln(k))/(\sqrt{k+2})}, with k starting at 1 and going to \infty Homework Equations Does this series converge or diverge? Be sure to explain what tests were used and why they are applicable. The Attempt at a Solution Okay, my TA got that this diverges, but I...
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    Trouble with a tangent series expansion

    Okay, so I am supposed to expand ln(cos(x)) basing my calculations on tan(x) = x + (1/3)x^3 + (2/15)x^5 + (17/315)x^7 + ... and expanding out to that fourth term is sufficient. I am having a major brain meltdown, I can't seem to find any equivalencies present, and I'm sure there are. Any help...
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    Investigating Matter, Mass and Molecules

    Steel does not have molecules in it. Why do you keep thinking that?
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