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(a) Find the minimum and maximum of f(x, y, z) = x2 +y2 +z subject to the constraint x2 +2y2 +4z2 = 1.
(b) Suppose the constraint was changed to x2 + 2y2 + 4z2 = 1.5. Without re-solving the problem under the new constraint, estimate the maximum value of f under the new constraint.
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Find the approximations T10, M10, and S10 for 0∫π 38 sinx dx. Find the corresponding errors ET, EM, and ES. How large do we have to choose n so that the approximations Tn, Mn, and Sn to the integral in part (a).
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Find the particular solution that satisfies the initial condition. (Enter your solution as an equation.)
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