. Let f(x) = x [0, 2]. - Let f(x) = { 0 1 9...

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. Let f(x) = x € [0, 2]. - Let f(x) = { 0 1 9 9 x € [0, 1] x € (1,2]. x² sin x-² 0 Show that f € R[0, 2], ƒ has no antiderivative on [0,2], and find F(x) = f(t)dt for x € (0, 1] x = 0. 9 there. What does this example mean? . Let f' be continuous on [0, ∞) with f(0) = 1. If f* f'(t)dt = f* f(t)dt for all x > 0, show that f(x) = e* for all x > 0. Find f'. Then f' has an antiderivative but f' is not in R[0, 1] since f' is unbounded . Let f(x) = x € [0, 2]. - Let f(x) = { 0 1 9 9 x € [0, 1] x € (1,2]. x² sin x-² 0 Show that f € R[0, 2], ƒ has no antiderivative on [0,2], and find F(x) = f(t)dt for x € (0, 1] x = 0. 9 there. What does this example mean? . Let f' be continuous on [0, ∞) with f(0) = 1. If f* f'(t)dt = f* f(t)dt for all x > 0, show that f(x) = e* for all x > 0. Find f'. Then f' has an antiderivative but f' is not in R[0, 1] since f' is unbounded

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The image contains three separate problems related to functions their Riemann integrability differentiability antiderivatives and some specific proper... View the full answer