Suppose the two curves r(t) = (t,0, 1 + e' sin(t)) and q(s) = (0, s, vs² + 1) lie entirely on the graph of some unknown function f(x, y). Find the equation of the tangent plane to the graph of f at the point (0,0, 1). %3D

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
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Suppose the two curves **r**(t) = ⟨t, 0, 1 + e^t sin(t)⟩ and **q**(s) = ⟨0, s, √(s² + 1)⟩ lie entirely on the graph of some unknown function *f*(x, y). Find the equation of the tangent plane to the graph of *f* at the point (0, 0, 1).
Transcribed Image Text:Suppose the two curves **r**(t) = ⟨t, 0, 1 + e^t sin(t)⟩ and **q**(s) = ⟨0, s, √(s² + 1)⟩ lie entirely on the graph of some unknown function *f*(x, y). Find the equation of the tangent plane to the graph of *f* at the point (0, 0, 1).
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