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Let g(x, y) = 3x + ylny-sin(1-x). Suppose z is a differentiable function of x and y implicitly defined by the equation E:2 + y² = g(x, y) - 2. a. Find the instantaneous rate of change of g as one moves from the point (1, e) toward the point (e, 1). b. Find the equation of the tangent plane to the graph of E at (1, e, 1). c. If in addition, x and y are functions of r and t given by x = -rt multivariate chain rule to evaluate when r = -1 and t = 1. əz ət and y = er+2t, use

Let g(x, y) = 3x + ylny-sin(1-x). Suppose z is a differentiable function of x and y implicitly defined by the equation E:2 + y² = g(x, y) - 2. a. Find the instantaneous rate of change of g as one moves from the point (1, e) toward the point (e, 1). b. Find the equation of the tangent plane to the graph of E at (1, e, 1). c. If in addition, x and y are functions of r and t given by x = -rt multivariate chain rule to evaluate when r = -1 and t = 1. əz ət and y = er+2t, use

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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Let g(x, y) = 3x + ylny-sin(1-x). Suppose z is a differentiable function of x and y implicitly defined by the equation E: 2 + y² = g(x,y) - 2. a. Find the instantaneous rate of change of g as one moves from the point (1, e) toward the point (e, 1). b. Find the equation of the tangent plane to the graph of E at (1, e. 1). c. If in addition, x and y are functions of r and t given by x = -rt and y = er+²t, use дz multivariate chain rule to evaluate when r = -1 and t = 1.
Transcribed Image Text:Let g(x, y) = 3x + ylny-sin(1-x). Suppose z is a differentiable function of x and y implicitly defined by the equation E: 2 + y² = g(x,y) - 2. a. Find the instantaneous rate of change of g as one moves from the point (1, e) toward the point (e, 1). b. Find the equation of the tangent plane to the graph of E at (1, e. 1). c. If in addition, x and y are functions of r and t given by x = -rt and y = er+²t, use дz multivariate chain rule to evaluate when r = -1 and t = 1.
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