In Exercises 33–38, find the linearization
Chapter 13, Problem 37E(choose chapter or problem)
Bounding the Error in Linear Approximations In Exercises 33-38, find the linearization \(L(x, y)\) of the function \(f(x, y)\) at \(P_{0}\). Then find an upper bound for the magnitude \(|E|\) of the error in the approximation \(f(x, y) \approx L(x, y)\) over the rectangle \(R\).
\(f(x, y)=e^{x} \cos y\) at \(P_{0}(0,0)\),
\(R:|x| \leq 0.1,\ |y| \leq 0.1\)
(Use \(e^{x} \leq 1.11\) and \(|\cos y| \leq 1\) in estimating \(E\).)
Equation Transcription:
L(x,y)
f(x,y)
P0
|E|
f(x,y) approx L(x,y)
R
f(x,y)=ex cos y at P0 (0,0)
R: |x| ≤ 0.1, |y| ≤ 0.1
ex ≤ 1.11
|cosy| ≤ 1
E
Text Transcription:
L(x,y)
f(x,y)
P_0
|E|
f(x,y)≈L(x,y)
R
f(x,y)=e^x cos y at P_0(0,0)
R: |x| ≤ 0.1, |y| ≤ 0.1
e^x ≤ 1.11
|cosy| ≤ 1
E
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