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hw8ans - O to P is orthogonal to the plane 15.1(24 0(28 e...

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Math 20C Prof. Fitzsimmons Answers to even-numbered exercises from sections 14.8, 15.1 § 14.8 (16) x = y = z = 25, and the maximum volume is 15 , 625 cm 3 . (26) Use Lagrange multipliers with f ( x, y, z ) = x 2 + y 2 + z 2 and g ( x, y, z ) = ax + by + cz - d . The closest point is P = d a 2 + b 2 + c 2 · a, b, c . The distance from this point P to the origin O is d/ a 2 + b 2 +
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Unformatted text preview: O to P is orthogonal to the plane. § 15.1 (24) 0 (28) e 2-1 2 · e 6-1 3 = e 8-e 6-e 2 + 1 6 . (38) ( e 2-1) · (1-√ 2 / 2) (44) The given integral is equal to R 1 ln(1 + y ) dy , which is equal to 2 ln 2-1....
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