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Let F(x, y, z) Find an equation for the tangent plane to the level surface F(x, Y, z) = 8 (an ellipsoid in R³) at the point (xo, Yo, 2o) = (1,0, 0). 8x? + 2y? + 4z², which represents a three-dimensional surface in Rª.

Let F(x, y, z) Find an equation for the tangent plane to the level surface F(x, Y, z) = 8 (an ellipsoid in R³) at the point (xo, Yo, 2o) = (1,0, 0). 8x? + 2y? + 4z², which represents a three-dimensional surface in Rª.

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 \( F(x, y, z) = 8x^2 + 2y^2 + 4z^2 \), which represents a three-dimensional surface in \( \mathbb{R}^4 \). Find an equation for the tangent plane to the level surface \( F(x, y, z) = 8 \) (an ellipsoid in \( \mathbb{R}^3 \)) at the point \( (x_0, y_0, z_0) = (1, 0, 0) \).
Transcribed Image Text:Let \( F(x, y, z) = 8x^2 + 2y^2 + 4z^2 \), which represents a three-dimensional surface in \( \mathbb{R}^4 \). Find an equation for the tangent plane to the level surface \( F(x, y, z) = 8 \) (an ellipsoid in \( \mathbb{R}^3 \)) at the point \( (x_0, y_0, z_0) = (1, 0, 0) \).
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