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We learned in class that if f(x, y) is a function of two variables, that Vf(a, b) is perpendicular / normal to the tangent line of the level curve f(x, y) k, where k = f(a, b). Similarly, if g(r, y, z) is a function of three variables, then Vg(a, b, c) is normal to the tangent plane of the level surface g(r, y, z) = k, where k = g(a, b, c). Use this information to easily find an equation of the tangent plane to the surface ry – y² + 2x²z = 4 at the point (1, 2, 3). %3D %3D

We learned in class that if f(x, y) is a function of two variables, that Vf(a, b) is perpendicular / normal to the tangent line of the level curve f(x, y) k, where k = f(a, b). Similarly, if g(r, y, z) is a function of three variables, then Vg(a, b, c) is normal to the tangent plane of the level surface g(r, y, z) = k, where k = g(a, b, c). Use this information to easily find an equation of the tangent plane to the surface ry – y² + 2x²z = 4 at the point (1, 2, 3). %3D %3D

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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P We learned in class that if f(r, y) is a function of two variables, that Vf(a, b) is perpendicular / normal to the tangent line of the level curve f(x, y) k, where k = Vg(a, b, c) is normal to the tangent plane of the level surface g(x, y, z) = k, where k = g(a, b, c). Use this information to easily find an equation of the tangent plane to the surface ry – y² + 2x2z = 4 at the point (1, 2, 3). f(a, b). Similarly, if g(x, y, z) is a function of three variables, then %3D -
Transcribed Image Text:P We learned in class that if f(r, y) is a function of two variables, that Vf(a, b) is perpendicular / normal to the tangent line of the level curve f(x, y) k, where k = Vg(a, b, c) is normal to the tangent plane of the level surface g(x, y, z) = k, where k = g(a, b, c). Use this information to easily find an equation of the tangent plane to the surface ry – y² + 2x2z = 4 at the point (1, 2, 3). f(a, b). Similarly, if g(x, y, z) is a function of three variables, then %3D -
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