question archive Type B Problems B3

Type B Problems B3

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Type B Problems B3.1. Consider the function f : R x R - R defined by 0 f (x, y ) = (x, y) = (0, 0), sin (x ) sin(y) ac2 +y2 (a, y) + (0, 0). (a) Prove that g: R - R defined by g(x) = f(x, 0) is continuous when R is equipped with the distance d1. (b) Prove that the function f: (R2, dx) - (R, d1 ) is not continuous at (0, 0). R39 Prove lowing ons at all

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