Need some Multivariate and Vector Calculus help thanks?
Need some Multivariate and Vector Calculus help thanks?
Let R be the region given by R = {(x, y) ∈ R^2 : 0 ≤ x ≤ 1, 0 ≤ y ≤ 1}
For fixed n ∈ N set x_j = y_j = j/n , j = 1, 2, . . . , n.
Set J_kl = [x_k−1, x_k] × [y_l−1, y_l ] for 1 ≤ k, l ≤ n.
Define f : R → R by f (x, y) = xy and assume int int_R f (x, y) dxdy exists.
(a) Write down the area A_kl of the region J_kl in terms of n;
(b) Briefly describe why f is a continuous function on R;
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