Continuity and Uniform Continuity
13.p We can discover a Lipscitz inequality for the square root function f(x) = xin much the same way. Consider the function f(x) = p xde ned on the interval S= (a;1) where a>0. For x 1;x 2 2Sthe Mean Value Theorem says that p x 1 p x 2 = (x 1 x 2)=(2 p c) where cis between x 1 and x 2. If x 1;x 2 2S then c 2S (as cis between x 1 and x 2) and ...
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