(2) Consider the function f: R → R³ given by f(x, y, z, w)= (1+z+sin(z-2y), e, 2z+tan(w+z²)). (a) Find the quadratic app

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2 Consider The Function F R R Given By F X Y Z W 1 Z Sin Z 2y E 2z Tan W Z A Find The Quadratic App 1 (17.48 KiB) Viewed 8 times

(2) Consider the function f: R → R³ given by f(x, y, z, w)= (1+z+sin(z-2y), e, 2z+tan(w+z²)). (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(z-y), y cos(x²-1)). We can compose the maps f and g to obtain a smooth function gof: R¹ R². Use the chain rule to compute Dp (gofl. where P= (0,0,0,0)