9. (15 points) Let f(x) = Ï sin(w/k) k k=1 (a) Prove that f(x) is continuous on R. Hint: use a well known inequality | s

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9 15 Points Let F X I Sin W K K K 1 A Prove That F X Is Continuous On R Hint Use A Well Known Inequality S 1 (54.61 KiB) Viewed 31 times

9. (15 points) Let f(x) = Ï sin(w/k) k k=1 (a) Prove that f(x) is continuous on R. Hint: use a well known inequality | sin x| = |x| to show that the series converges uniformly on [-R, R) for any R > 0. You do not have to prove this inequality. (b) Show that f(x) is differentiable on R. (c) Express $* $(t)dt as an infinite series.