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Posted: **Wed May 04, 2022 10:32 am**

: 3 Let F 0 1 R Be A Differntiable Function Suppose That F 0 0 And That F R 1 For Every X 0 1 A Prov 1 (15.93 KiB) Viewed 36 times

3. Let f: [0, 1] → R be a differntiable function. Suppose that f(0) = 0 and that f' (r) ≤1 for every x € (0,1). (a) Prove that the series ƒ² (+) converges. Hint: use Lagrange's theorem. (b) Conclude that the series arctan² () converges. n=1