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Mathematics 250 - Spring 2016

Homework

Section 7.2: 1, 2(a), 3, 4, 7

Also: Find the second-order Taylor polynomial for each of the following:

  1. $f(x, y, z) = 4xyz + 6xy^2 + 4x^2z^2$ at $(1, -1, 1)$
  2. $f(x, y, z) = e^{x + y + z}$ at $(0, 0, 0)$

Answers:

  1. $p(x, y, z) = 6 + 10(x - 1) - 8(y + 1) + 4(z - 1) + 8(x - 1)^2 \\+ 6(y + 1)^2 + 4(z - 1)^2 - 8(x - 1)(y + 1) + 4(y + 1)(z - 1) + 12(x - 1)(z - 1)$
  2. $p(x, y, z) = 1 + x + y + z + \frac{1}{2}x^2 + \frac{1}{2}y^2 + \frac{1}{2}z^2 + xy + xz + yz$