Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN: 9780470458365
Author: Erwin Kreyszig
Publisher: Wiley, John & Sons, Incorporated
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a) Compute the equation of the tangent plane to the level surface
g(x, y, z) = x'y + 2y°z – 3z*x = 3
Don't round answers unless
at the point (1,0, – 1).
b) Consider z = z(x, y) as a function of x and y, so z(1,0) = -1. Use
the approximation of the surface by its tangent plane to approximate
21 = z(0.99, 0.02).
c) Use your approximation of z1 from part b to evaluate g(0.99, 0.02, zı)
to five decimal places. Your answer should be close to 3. Is it?
the instructions request approximations, or as part of checking your
own work.
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Transcribed Image Text:a) Compute the equation of the tangent plane to the level surface g(x, y, z) = x'y + 2y°z – 3z*x = 3 Don't round answers unless at the point (1,0, – 1). b) Consider z = z(x, y) as a function of x and y, so z(1,0) = -1. Use the approximation of the surface by its tangent plane to approximate 21 = z(0.99, 0.02). c) Use your approximation of z1 from part b to evaluate g(0.99, 0.02, zı) to five decimal places. Your answer should be close to 3. Is it? the instructions request approximations, or as part of checking your own work.
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