Answer to Question #72271 in Calculus for Lastone

Question

6. Find the absolute minimum of f(x, y) = x
2 + y
2 + 2y − 1 on D = {(x, y)|x
2 +
y
2
4 ≤ 1}
7. Use Lagrange multipliers to find the maximum and minimum values of the function
subject to the given constraint(s).
a) f(x, y, z) = xyz; x
2 + 2y
2 + 3z
2 = 6
b) f(x, y, z) = yz + xy; xy = 1, y2 + z
2 = 1
8. Find the first four terms in the Taylor series expansion of the function:
f(x, y) = e
−y
2
cos(x + y) about the point (0, 0).

Answer 1

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