Recent content by crybllrd

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    Mass Observed to Increase as Velocity Increases?

    With CERN's Large Hadron Collider being in the news recently, I began to think of a question that bothered me for years about particle accelerators. It is well known in physics that mass increases as velocity does (Special Relativity if I'm not mistaken), so if these particles in the LHC are...
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    Limit Evaluation

    Ah, ok, I got -1/6. I don't remember why exactly I didn't get a good answer on the exam, but I think I was on like my 6th L'Hopital iteration and wasn't willing to spend any more time on a 4 point problem. Thanks guys, now I can rest easy this summer, as my brain is completely fried now!
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    Limit Evaluation

    How did you get the sin(x)2 in the denominator? If I multiply x2by xsin(x) I get x3sin(x).
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    Limit Evaluation

    Homework Statement I had an exam last night and I was stuck on this problem. I went home where I had more time (and resources) and still can't figure it out, and I won't get my exam back (it was a final). \lim_{x\to0}\frac{1}{x^{2}}-\frac{1}{xsinx} Homework Equations The...
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    Which trig sub do I use?

    Homework Statement \int\frac{dx}{x(x^{2}-1)^{3/2}} Homework Equations The Attempt at a Solution I know I need to use trig sub, but which form? I can't seem to find any that fit this form.
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    Show that the Gamma function is converging

    Never mind, I figured it out with a comparison test. Funny, after I post things on here I always seem to figure them out on my own. Well, whatever works!
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    Show that the Gamma function is converging

    Homework Statement The gamma function, which plays an important role in advanced applications, is defined for n\geq1 by \Gamma(n)=\int_0^{\infty} t^{n-1}e^{-t}dt (a) Show that the integral converges on n\geq1 (b) Show that \Gamma(n+1)=n\Gamma(n) (c) Show that \Gamma(n+1)=n! if n\geq1 is an...
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    Electric Potaential of two spheres

    Never mind, I figured it out. Thanks a lot!
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    Electric Potaential of two spheres

    101e5 tells me that I am off by a multiple of ten. I am still confused though- in my calculator I put in (K*6.75*10e-6)/6e-2 (I have K stored as the ke constant) and get 101. It sounds like you're telling me that my calculator cannot handle scientific notation, and I need to tag on the "...
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    Electric Potaential of two spheres

    Thanks for the quick reply. v1=kq1/r1 v1=8.99e9 Nm2/C2*1.95e-5C/6e-2m v1=101 Nm/C Nm/C is a V
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    Electric Potaential of two spheres

    Homework Statement Electric charge can accumulate on an airplane in flight. You may have observed needle-shaped metal extensions on the wing tips and tail of an airplane. Their purpose is to allow charge to leak off before much of it accumulates. The electric field around the needle is much...
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    Show that it satisfies the differential equation

    Alright I just did both. Thanks again.
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    Show that it satisfies the differential equation

    Ugh, this problem is killing me. On a later part, it asks: Let v(t) be the velocity of a falling object of mass m that started from rest. For large velocities, air resistance is proportional to the square of velocity v(t)2. If we choose coordinates so that v(t)>0 for a falling object, then...
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    Show that it satisfies the differential equation

    Cool, thanks a lot. I think I'm definitely ready for an exam on Monday. EDIT: I had a math error on my last post when I substituted for y2. When done properly, all the A's cancelled out.
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    Show that it satisfies the differential equation

    Oh ok I get it. On part A I algebraically rearranged to get dy/(1-y^2 )=dt, then I integrated both sides to get (after simplification) y= tanh⁡t, done. Just did it the long way, not even thinking because all the other problems were integration. then, when I started integrating part b...
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