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5. Find the equations of the tangent plane and the normal line to the surface cos(x)-x²y+ez+yz = 4 at the point (0, 1, 2). What is, approximately, the z-coordinate of the point (-0.1, 0.9, z) on this surface?

5. Find the equations of the tangent plane and the normal line to the surface cos(x)-x²y+ez+yz = 4 at the point (0, 1, 2). What is, approximately, the z-coordinate of the point (-0.1, 0.9, z) on this surface?

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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**Problem 5:** Find the equations of the tangent plane and the normal line to the surface \( \cos(\pi x) - x^2 y + e^{xz} + yz = 4 \) at the point \( (0, 1, 2) \). What is, approximately, the \( z \)-coordinate of the point \( (-0.1, 0.9, z) \) on this surface?
Transcribed Image Text:**Problem 5:** Find the equations of the tangent plane and the normal line to the surface \( \cos(\pi x) - x^2 y + e^{xz} + yz = 4 \) at the point \( (0, 1, 2) \). What is, approximately, the \( z \)-coordinate of the point \( (-0.1, 0.9, z) \) on this surface?
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