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###### Question 3 [3 points]Give a counterexample to show the following form is invalid.P or Q P and Q

Question 3 [3 points] Give a counterexample to show the following form is invalid. P or Q P and Q

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1 Consider the variational problem of finding the stationary curves of the functional integral I = Flys Y , r)dz = Ily(z)] . The Icsulting Euler-Lagrange equation for y(z) is given by 9F ( 8F =0 _ dy (a) Consider the special case of a function F that does not explicitly depend O I Derive the resulti...

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point) Take the Laplace transform of the following initia value and solve for Y(s) = L{y(t)}: J' +4y = sin(xt), 0 St< 1 1 <1 %(0) = 0, Y(0) = 0 Y(s) Hint: write the right hand side in terms of the Heaviside function (Use step(t-c) for u (t) .) Note: Now find the inverse transform to find ...

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