Exercise 2. Determine whether the sequence of functions (fn)n converges uniformly on S. 1 S = [0, 1]. S = [0, 1]. fn (x) = 1+ (nx – 1)²' fn(x) = na" (1 – x),

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Q: 1. Function f is continuous on (-00,00). Find constant k. f(x) [kx² + 2x x-kx if x ≥ 2 if x < 2

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Q: Let fn(x) x + n a. Show that fn(x) converges pointwise [0, 0). on

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Q: Is g(x) = ln( x2+2 ) uniformly continuous on the interval (−∞,∞)?

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Sequence and Series

A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence.  It was invented by German mathematician Carl Friedrich Gauss.