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