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(2) Consider the function f: R¹ R³ given by f(x, y, z, w) = (1+x+ sin(z − 2y), eyz-w, 2z+tan(w+x²)). (a) Find the quadra
Posted: Wed Jul 06, 2022 1:21 pm
by answerhappygod
- 2 Consider The Function F R R Given By F X Y Z W 1 X Sin Z 2y Eyz W 2z Tan W X A Find The Quadra 1 (48.27 KiB) Viewed 13 times
(2) Consider the function f: R¹ 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 - 2²-1)). 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)