Recent content by mikeyrichster

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    Vector calculus

    Hi there! thanks for your help sorry about the fraction thing.. what i ment was that it is a vector but written vertically not horizontally... so still a vector but not (y^2, 2xy) .. Im damn useless at LaTeX so i cant make it with a large bracket and the y^2 at the top and the 2xy at the...
  2. M

    Greens Theorem

    The Integral I is defined by I = Integral F . dr Where F = (x-y, xy) << This is a verticle vector, i just didn'nt know how to write it with latex. And C is a triangle with the vertices (0,0), (1,0) and (1,3) tracked anticlockwise. Calculate the line integral using greens...
  3. M

    Vector calculus

    Hi there, thanks for your help! Is the expression you refer to the arc length formula? you said "therefore the total distance will be the integral from t = 0 to 1 of |r'(t)|dt." does that mean the integral from 0 to 1 of the absolutle vaule of r(t) differentiated? How do you integrate...
  4. M

    Vector calculus

    Homework Statement A force is applied to a particle, defined by: F(x,y)= (y^2, 2xy) << This is a verticle bracket with the y^2 ontop of the 2xy The path of the particle is straight. The particle moves from (-1,2) to (1,3) i) Calculate the work that the force F does as the...
  5. M

    Vector calculus

    Im afraid my use of LaTeX code, sucks. My apologies to anyone friendly enough to help! The problem: A string takes a path shown by the equation below: r(t)=(t,3t^2,6t^3) Where the RHS is a verticle vector (didnt know how to code this!) and 0 <= t <= 1 The mass per unit length...
  6. M

    Find all critical and stationary points: Legrange multipliers

    Thanks for all your help, Ive finally got my head around this... and cheers for the LaTeX heads up. Ive spent ages looking for good LaTeX resources for beginners. :)
  7. M

    Find all critical and stationary points: Legrange multipliers

    Hey thanks for your help thats brilliant! So I have the solvable system of EQ's: -2y = 2y\lambda and 3x^2=2x\lambda Am I correct in saying now that x = -2/3 and y = +/-sqrt 13/9 ? sorry about my lack of LaTeX typesetting. :)
  8. M

    Find all critical and stationary points: Legrange multipliers

    Find all critical and stationary points of the function f(x,y)=x^3-y^2 subject to the inequality constraint c(x,y)=1-x^2-y^2 >=0 So far ive deduced that I need to use a lagrange multiplier L say, so i think i need to solve the equations : 3x^2=-2Lx -2y^2=-2Ly and 1-x^2-y^2 >=0 Is...
  9. M

    Reversing the order of integration

    Hi Im trying to evaluate a line integral, and i need to reverse the order of integration, i'll call the function f(x) as it doesnt matter too much. and the bounds are: double integral f(x) dxdy where inner integral is from x=y^2/a to x=y and the outer integral is from y=0 to y=a (where a is a...
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