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Consider the function given as example in lecture: f(x, y) = (e x cos(y), ex sin(y))...

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Advance Math

Consider the function given as example in lecture: f(x, y) = (ex cos(y), ex sin(y)) (6.2) Denote a = (0, π/3) and b = f(a). Let f−1 be a continuous inverse of f defined in a neighborhood of b.Find an explicit formula for f −1 and compute Df−1 (b). Comparethis with the derivative formula given by the Inverse FunctionTheorem.

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