(2) Consider the function f : R¹ → R³ given by f(x, y, z, w) = (1 + x + sin(z − 2y), eªz−w, 2z + tan(w + x²)). (a) Find

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2 Consider The Function F R R Given By F X Y Z W 1 X Sin Z 2y Eaz W 2z Tan W X A Find 1 (84.46 KiB) Viewed 10 times

(2) Consider the function f : R¹ → R³ given by f(x, y, z, w) = (1 + x + sin(z − 2y), eªz−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 ƒ(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 g o f : Rª → R². Use the chain rule to compute Dp(gof), where P = (0, 0, 0, 0)