Proof Prove that the angle of inclination of the tangent plane to the surface at the
Chapter 13, Problem 67(choose chapter or problem)
Prove that the angle of inclination \(\theta\) of the tangent plane to the surface z = f(x, y) at the point \(\left(x_{0}, y_{0}, z_{0}\right)\) is given by
\(\cos \theta=\frac{1}{\sqrt{\left[f_{x}\left(x_{0}, y_{0}\right)\right]^{2}+\left[f_{y}\left(x_{0}, y_{0}\right)\right]^{2}+1}}\).
Text Transcription:
theta
(x_0, y_0, z_0)
cos theta =1} / sqrt [f_x (x_0, y_0)]^2 + [f_y (x_0, y_0)]^2 + 1
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