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1. Consider the system of equations x = uev + veu and y2 = v - u. Show that near (u, v, x, y) = (0,0,0,0), (u,v) can be expressed as a differentiable function of (x,y) and find the values of and . 2. Let b0, b1, b2, … be a sequence of nonnegative real numbers. If ∑ converges pointwise on [0,1) to a bounded function g(x). Prove that ∑ converges.

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