5. Let f [0,2] R be defined by x, 0 < x < 1 f(x) = x+1 1≤x≤2 (a) Explain why ƒ = R[0,2] by identifying the class of functions of belongs to. (b) Determine explicitly the function F(x) = * f(t)dt for x = [0,2]. (c) Find the subset {x: F is continuous at x} ≤ [0,2] with your justification. (d) Find the subset {x: F is differentiable at x} ≤ [0,2] with your justification.

5. Let f [0,2] R be defined by x, 0 < x < 1 f(x) = x+1 1≤x≤2 (a) Explain why ƒ = R[0,2] by identifying the class of functions of belongs to. (b) Determine explicitly the function F(x) = * f(t)dt for x = [0,2]. (c) Find the subset {x: F is continuous at x} ≤ [0,2] with your justification. (d) Find the subset {x: F is differentiable at x} ≤ [0,2] with your justification.

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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