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Let f(z)=u+iv be an analytic function, phi(u,v) any function with second order partial derivatives and g(u,v) any function with first order partial derivatives.
a) Let L_x,y be the Laplace operator in x,y coordinates and L_u,v be the Laplace operator in u,v coordinates. Show that L_x,y(phi o f)=L_u,v |f'(z)|^2
b)Let G_u,v be the gradient vector in u,v, and G_x,y be the gradient vector in x,y coordinates. Show that |G_x,y(g o f)|^2=|G_u,v(g)|^2 |f'(z)|^2 where the | | is the euclidean norm in C.
Integration by parts method - How much longer would the worm be at t = 2, if it always grew at the maximum rate? Use Integration by parts.
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The combined degrees of freedom
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Let f:R->R be a function that satisfies f(x+y) = f(x)+f(y) for all x,y in R. Suppose that f is continuous on R and that f(1)=k. Prove that f(x)=kx for all x in R.
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Find the true mean completion time of the task
Using the quadratic equation x2 - 6x + 8 = 0, perform the following tasks: Graph the function using the equation in part a. Explain why it is not necessary to plot points to graph when using y = a (x - h) 2 + k.
Application of the Binomial Distribution to an Aircraft. Suppose you are flying a four-engine aircraft on a 10-hour transoceanic flight. Assume that it has been established that the probability of an engine of the type you have on your aircraft fa..
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