Solution: find parametric equations for the line that is
Chapter , Problem 55PE(choose chapter or problem)
Linearizations In Exercises 55 and 56, find the linearization \({L}({x}, \ {y})\) of the function \({f}({x}, \ {y})\) at the point \(\mathrm{P}_{0}\). Then find an upper bound for the magnitude of the error \({E}\) in the approximation \(f(x, \ y) \approx L(x, \ y)\) over the rectangle \({R}\).
$${f}({x}, \ {y})=\sin \mathrm{x} \cos \mathrm{y}, \ \quad \mathrm{P}_0(\pi / 4, \pi / 4)$$
$$R:\left|x-\frac{\pi}{4}\right| \leq 0.1,\left|y-\frac{\pi}{4}\right| \leq 0.1$$
Equation Transcription:
Text Transcription:
L(x, y)
f(x, y)
P_0
E
f(x, y) approx L(x, y)
R
f(x, y) = sin x cos y, P_0(pi/4, pi/4)
R: |x - pi/4| leqslant 0.1, |y - pi/4| leqslant 0.1
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