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2. Suppose that X = Y = R2 and the metric d 1 is defined on X by d 1 ((x 1 , x 2
2. Suppose that X = Y = R2 and the metric d1 is defined on X by d1 ((x1, x2), (y1, y2)) = |x1 y1| + |x2 y2| and the metric d2 is defined on Y by d2 ((x1, x2), (y1, y2)) = max{|x1 y1|, |x2 y2|}. Suppose f is a function that maps the metric space (X, d1) to the metric space (Y, d2) is defined by f ((x1, x2)) = (3x1 5x2 + 2, 4x1 + 3x2 7) . (a) Write the definition of the limit of a function at a point in terms of metric spaces. (b) Use the definition of the limit of a function at a point on metric spaces to prove that
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