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Suppose you need to know an equation of the tangent plane to a surface S at the point P(3, 1, 3). You don't have an equation for S but you know that the curves r₁(t) = (3 + 3t, 1 t², 3 - 4t + t²) r₂(u) = (2 + u², 2u³1, 2u + 1) both lie on S. Find an equation of the tangent plane at P.

Suppose you need to know an equation of the tangent plane to a surface S at the point P(3, 1, 3). You don't have an equation for S but you know that the curves r₁(t) = (3 + 3t, 1 t², 3 - 4t + t²) r₂(u) = (2 + u², 2u³1, 2u + 1) both lie on S. Find an equation of the tangent plane at P.

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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Suppose you need to know an equation of the tangent plane to a surface S at the point P(3, 1, 3). You don't have an equation for S but you know that the curves r₁(t) = (3 + 3t, 1 - t², 3 - 4t + t²) r₂(u) = (2+ u², 2u³1, 2u+1) both lie on S. Find an equation of the tangent plane at P.
Transcribed Image Text:Suppose you need to know an equation of the tangent plane to a surface S at the point P(3, 1, 3). You don't have an equation for S but you know that the curves r₁(t) = (3 + 3t, 1 - t², 3 - 4t + t²) r₂(u) = (2+ u², 2u³1, 2u+1) both lie on S. Find an equation of the tangent plane at P.
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