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f(x, y, z, w) = (1+x+ sin(z − 2y), ez-w, 2z+tan(w+x²)).

f(x, y, z, w) = (1+x+ sin(z − 2y), ez-w, 2z+tan(w+x²)).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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(2) Consider the function f : R4 → R³ given by f(x, y, z, w) = (1 + x + sin(z − 2y), eyz-w, 2z+tan(w+x²)). (a) Find the quadratic approximation of f at the point P = (0, 0, 0, 0). Use this approximation to estimate the value f(0.1, -0.1, -0.1, 0.1). (b) Now consider the function g: R³ → R² given by g(x, y, z) = (sin(x - y), y cos(x² - z² – 1)). We can compose the maps f and g to obtain a smooth function go f: R¹ R². Use the chain rule to compute Dp (gof), where P = (0, 0, 0, 0)
Transcribed Image Text:(2) Consider the function f : R4 → R³ given by f(x, y, z, w) = (1 + x + sin(z − 2y), eyz-w, 2z+tan(w+x²)). (a) Find the quadratic approximation of f at the point P = (0, 0, 0, 0). Use this approximation to estimate the value f(0.1, -0.1, -0.1, 0.1). (b) Now consider the function g: R³ → R² given by g(x, y, z) = (sin(x - y), y cos(x² - z² – 1)). We can compose the maps f and g to obtain a smooth function go f: R¹ R². Use the chain rule to compute Dp (gof), where P = (0, 0, 0, 0)
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