(a) State the Implicit Function Theorem for an equation in the three variables x, y and...

  

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(a) State the Implicit Function Theorem for an equation in the three variables x, y and (2) (b) Consider the equation xyz = 4x² + y² = 2². Use the Implicit Function Theorem to show that the given equation has a smooth unique local solution of the form z = g(x, y) about the point (2,0,4). Then find the local linearization of g about the point (2,0). Hints: (a) State the Implicit Function Theorem for an equation in the three variables x, y and (2) (b) Consider the equation xyz = 4x² + y² = 2². Use the Implicit Function Theorem to show that the given equation has a smooth unique local solution of the form z = g(x, y) about the point (2,0,4). Then find the local linearization of g about the point (2,0). Hints:

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