Answer: Prove that the angle of inclination of the tangent plane to the surface at the
Chapter 13, Problem 77(choose chapter or problem)
Prove that the angle of inclination \(\boldsymbol{\theta}\) 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)
costheta=frac1sqrt[f_x
(x_0,y_0)]^2+[f_y(x_0,y_0)]^2+1
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