Need some Multivariate and Vector Calculus help thanks?

Posted on 2016-05-18 18:39:00 in Math by ALTEN

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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