The equation yz = 2ln(x + z) defines a surface S in R. The point P(0,0,1) is on the surface. (a) Write down the equation of the tangent plane to S at P. (b) The equation for S defines z implicitly as a function f of x and y. So f(0,0) = 1. The tangent plane to S at P is also the graph of the linearization of f(x,y) at (0,0). Use this linearization to find an approximate value for f(). When x = and y = , then z is approximately equal to

The equation yz = 2ln(x + z) defines a surface S in R. The point P(0,0,1) is on the surface. (a) Write down the equation of the tangent plane to S at P. (b) The equation for S defines z implicitly as a function f of x and y. So f(0,0) = 1. The tangent plane to S at P is also the graph of the linearization of f(x,y) at (0,0). Use this linearization to find an approximate value for f(). When x = and y = , then z is approximately equal to

Algebra & Trigonometry with Analytic Geometry

13th Edition

ISBN:9781133382119

Author:Swokowski

Publisher:Swokowski

Chapter3: Functions And Graphs

Section3.3: Lines

Problem 22E

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