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Question 1 (15 marks, C3) Let I be the rectangle [0, 5] × [0, 5] in the plane R². Define the function f : I → R by f(x,
Posted: Mon Jul 11, 2022 12:44 pm
by answerhappygod
- Question 1 15 Marks C3 Let I Be The Rectangle 0 5 0 5 In The Plane R Define The Function F I R By F X 1 (102.57 KiB) Viewed 22 times
Question 1 (15 marks, C3) Let I be the rectangle [0, 5] × [0, 5] in the plane R². Define the function f : I → R by f(x, y) = Y, X, y > x, y ≤ x. For k ≥ 3, let P be the regular partition of [0, 5] into k partition intervals, and let Pk = (Pk, Pk) be the corresponding partition of I. (a) Evaluate U(f, Pk) and L(f, Pk) for each k ≥ 3. (b) Find the limits lim U(ƒ, Pk) and_lim_L(ƒ, Pk). k→∞x k→∞ (c) Use your result in part (b) to conclude that f : I→ R is integrable and find f. [10] [3] [2]