Homework Assignment 6.2 PDF

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Professor Jason Samuels

Homework Assignment 6.2...

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HW 6.2 – The tangent plane & differentials For each function, find (a) the equation of the tangent plane, written in two notations: z-z0 & L(x,y) (b) the formula for dz (d) the approximation for the function value at the nearby point using the linear formula (e) for the linear approximation, find ΔL between the two points; also, how much of ΔL was due to change in x (call it ΔxL) and how much was due to change in y (call it ΔyL) (f) the exact function value at the nearby point and the change in the actual function value, call it Δf 1. z = x2y3 at the point (-1,3) and nearby point (-0.9, 3.2) 2. z = exsin(y) at the point (0,0) and nearby point (.07, -.03) 3. z = (x2+y2)-1 at the point (1,2) and the nearby point (1.1, 1.8)...