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  1. S

    Solution to general IVP

    Bump...any suggestions?
  2. S

    Solution to general IVP

    Homework Statement Find all solutions of the IVP y'' + a(t)y' + b(t)y = 0, y(t0) = 0, y'(t0) = 0 where t0 is any fixed point on the t-axis and the coefficients are continuous. The Attempt at a Solution I know this has to do with the Existence and Uniqueness theorem. How would I apply...
  3. S

    Differential Equations - Exponential Decay

    These are what I think I'm not sure how to find graph solutions from my equation: y = 4 + Ce^(-.5t) Thanks for your help!
  4. S

    Differential Equations - Exponential Decay

    So...first interval - exponentially decreasing graph when y = R/k, it's a constant, straight line along R/k? and when y is big, it's increasing?
  5. S

    Differential Equations - Exponential Decay

    Homework Statement We have the ODE y' = -ky + R for a population y(t) where death rate exceeds birth rate, counteracted by a constant restocking rate. I'm assuming k is the decay constant and R is the restocking rate The population at time t0 = 0 is y0, and I have to find a formula for...
  6. S

    Line Integral

    Ok thanks! But what if it's something like F(x,y,z)=(xy, x/z, y/z) ? Then if you plug in 0, you get a denominator of zero...
  7. S

    Line Integral

    Homework Statement What is the line integral of F(x,y,z) = (xy, x, xyz) over the unit circle c(t) = (cost, sint) t E (0,2pi) ? Homework Equations integral= (f(c(t))*c'(t))dt) The Attempt at a Solution Ok, so I tried solving this like I would any other line integral using the given...
  8. S

    Integration of a function.

    ohh....but how is the triple integral from 0 to 4-x^2-y^2 ? I know it's the function, but graphically, I don't understand. Oh well, my homework was due 10 minutes ago and I just turned it in (leaving this question blank) lol. Thanks for the answer though!
  9. S

    Integration of a function.

    Homework Statement Hey guys, I have one question: how can I integrate the function f(x,y,z)=x + y + z over the region between the paraboloid 4-x^2-y^2 and the xy-plane? Homework Equations For the paraboloid region, I used polar coordinates and found the volume of the region to be 8pi...
  10. S

    Volume of region R between paraboloid and xy-plane

    Alright, I used polar coordinates, i think, I got 8pi.
  11. S

    Volume of region R between paraboloid and xy-plane

    Would it be plus/minus sqrt(4-x^2) ?
  12. S

    Volume of region R between paraboloid and xy-plane

    Ok, for my limits, i got x is between 0 and 2, and y is between 0 and 2...so i did a double integral and got 16/3. Is that right?
  13. S

    4-ball B^4

    buuumppp...please help! Any advice is good!
  14. S

    4-ball B^4

    Homework Statement What is the x-simple description of a 4-ball = { ||x|| \leq r } Homework Equations It's a 4-ball, so isn't the equation x^{2} + y^2 +z^2 +w^2 ? The Attempt at a Solution For my limits, I got x is between \pm \sqrt{1-z^2} and y is between -1 and 1, and z is...
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    Volume of region R between paraboloid and xy-plane

    Umm, isn't the equation just z=4-x^2-y^2 ? Ok, thanks, I'll try a double integral, so for the limits, I would just set z=0, right? and solve for x and y?
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    Volume of region R between paraboloid and xy-plane

    Homework Statement So my question is: what is the volume of the region R between the paraboloid 4-x^2-y^2 and the xy-plane? Homework Equations I know how to solve it, it is a triple integral, but how do you find the limits of integration? The Attempt at a Solution Do I set x=0...
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    Gradient fields?

    Does anyone know how to draw a gradient field? For example, how do you draw one of f(x,y)=xy^2
  18. S

    Equation of 3-dimensional plane

    Ok thanks! Yeah, it was a typo, I meant -10.
  19. S

    Equation of 3-dimensional plane

    bump...can anyone please see if I am right or wrong??
  20. S

    Equation of 3-dimensional plane

    Homework Statement Find the equation of the plane through vectors u=(1,1,2) parallel to the plane containing v=(2,2,-1), w=(1,-1,0), and the origin. Homework Equations The Attempt at a Solution I did the cross product of v x w = (-1,-1,-4). Thus, my equation became -x-y-4z=-9...
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