Say how to linearize a function f[x, y] at a point {a, b}, and discuss how well the linearized version of f[x, y] at {a, b} approximates f[x, y] near {a, b}. Does the quality of the approximation improve or deteriorate as you go closer and closer to {a, b}

Step-by-step explanation:

Say how to linearize a function f[x, y] at a point {a, b}, and discuss how well the linearized version of f[x, y] at {a, b} approximates f[x, y] near {a, b}. Does the quality of the approximation improve or deteriorate as you go closer and closer to {a, b}

Linear  function f[x, y] at a point {a, b}

using taylor series at a point {a, b}

The quality of linearization improves as we goes close to point {a, b}

Since,

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