Recent content by NWeid1

  1. N

    (Calc 3) Finding mass of a wire using line integral

    Homework Statement Find the mass of a wire in the shape of the parabola y=x2 for 1 \leq x\leq2 and with density p(x,y)=x. Homework Equations The Attempt at a Solution I just want to make sure I am setting this integral up right. Here is what I did: I parameterized the equation to x=t, y=t2...
  2. N

    Surface area of x = ln(y) - y^2/8 from 1 to e

    oh ok. I took the derivative of x = lny - \frac{y^2}{8} and got x = \frac{1}{y} - \frac{1}{4y} and squared it to get \frac{1}{y^2} - \frac{1}{2y^2} + \frac{1}{16y^2} which is \frac{16}{16y^2} - \frac{8}{16y^2} + \frac{1}{16y^2} which is \frac{9}{16y^2}
  3. N

    Surface area of x = ln(y) - y^2/8 from 1 to e

    That was the equation that my prof. gave me, lol
  4. N

    Surface area of x = ln(y) - y^2/8 from 1 to e

    Homework Statement Find the area of the surface obtained from rotating the curve x = ln(y) - y^2/8 on [1,e] about the y-axis. Homework Equations SA = \int 2\pi*(f(x))*\sqrt{1+[f'(x)]^2}dx The Attempt at a Solution SA = \int 2\pi*(ln(y) - \frac{y^2}{8}))*\sqrt{1+\frac{9}{16*y^2}}dy from 1 to e...
  5. N

    Integrating ∫cos(x)^2*tan(x)^3dx using u-substitution and integration by parts

    Homework Statement ∫cos(x)^2*tan(x)^3dxHomework Equations The Attempt at a Solution Were learning Integration by parts and u substitution but this one I can't figure out. I tried making it ∫cos(x)*(sin(x)^3)/(cos(x)^3)dx and then ∫tan(x)*sin(x)^2 but I don't know if I'm going in the right...
  6. N

    Assume light travels from point a to b. Find the total time to get from a to b

    Haha sorry, didn't mean to break the calculus rules...-.-
  7. N

    Can someone explain this proccess for expressing limits as an integral?

    Oh, yeah I learned all the riemann sums.
  8. N

    EVT and Fermats to prove f'(c)=0

    f will be decreasing on (a,o) and increasing on (0,b)
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    EVT and Fermats to prove f'(c)=0

    Well, I first tried to use IVT but I was having a hard time to I talked to my prof. and he said to use extreme value theorem and fermats theorem. So, by EVT, I know that f will have an aboslute maximum and absolute minimum on [a,b]. By f'(a)<0<f'(b) I know that f will be decreasing and...
  10. N

    EVT and Fermats to prove f'(c)=0

    no one?
  11. N

    Can someone explain this proccess for expressing limits as an integral?

    You mean familiar with the process of converting an integral to a limit? I learned it but that is kind of what I'm asking. The only notes I have on this is what I have above, which I can't understand by the example.
  12. N

    Assume f(0)=f'(0)=0, prove there exists a positive constant such that f(x)>o

    Ok. I got it now. So now I'm confused. I see now that i used f(a)>0 and a>0 to prove that f(a)>0 lol...But, since f''(0)>0, f'(x) will be increasing at 0, right? And if f'(0)=0 and it is increasing, when x>0 for x near 0, f'(x)>0. Is this right at all? lol
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    Can someone explain this proccess for expressing limits as an integral?

    Well this is exactly what I have in my notes, and I know the answer is = \int\limits_{0}^{1}\sin{x}\, dx But I was just writing it down when he was teaching it, I never really understood the process.
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    Assume f(0)=f'(0)=0, prove there exists a positive constant such that f(x)>o

    Yeah but since we're only looking at x>0, wouldn't it work? So confused, ugh! lol
  15. N

    Assume f(0)=f'(0)=0, prove there exists a positive constant such that f(x)>o

    Ok, I think I got it. If a>0, and f''(0)>0 means f'(0) will be increasing so f'(x)>0 which means f(x) is increasing the origin and therefore f(x)>0. And since a>0 and f(a)>0 f'(c) = f(a)/a > 0 and therefore f(a) > 0. Is this right?