Engineering Calculus Notes 365

Engineering Calculus Notes 365 - 353 3.7. HIGHER...

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Unformatted text preview: 353 3.7. HIGHER DERIVATIVES • The exact value is f 0.1, π 2 = e0.2 cos π = 0. 2 • The linearization (degree one Taylor polynomial) gives an estimate of π T(0, π ) f 0.1, 6 3 √ 3 2 1 = + 0.1 − 2 π ≈ 0.14655. 6 • The quadratic approximation (degree two Taylor polynomial) gives π 1 0.1, = + 0.1 − 6 2 √ 3 2 + (0.1)2 − T2 f π 0, 3 1π 46 π 6 2 − √ ≈ −.00268 a much better approximation. As a second example, consider the function f (x, y, z ) = x2 y 3 z which has fx = 2xy 3 z, fy = 3x2 y 2 z, fz = x2 y 3 fxx = 2y 3 z, fxy = 6xy 2 z, fxz = 2xy 3 fyy = 6x2 yz, fyz = 3x2 y 2 fzz = 0. 3(0.1) π 6 ...
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This note was uploaded on 10/20/2011 for the course MAC 2311 taught by Professor All during the Fall '08 term at University of Florida.

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