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 ?L between the two points; also, how much of ?L was

due to change in x (call it ?xL) and how much was due to change in y (call it ?yL) (f) the exact function value at the nearby point and the change in the actual function value, call it ?f

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)

HW 6.2 The tangent plane & differentials For each function, nd (a) the equation of the tangent plane, written in two notations: 2-29 8: 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, nd AL between the two points; also, how much of AL was due to change in x (call it AL) and how much was due to change in y (call it AYL) (f) the exact function value at the nearby point and the change in the actual flmction value, call it Af 1. z = xzyJ at the point (-1,3) and nearby point (-0.9, 3.2) 2. z = e"sin(y) at the point (0,0) and nearby point (.07, -.03) 3. z = (xHy'l)'1 at the point (1,2) and the nearby point (1.1, 1.8)