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SOLVED:Prove that the absolute value function |x| is continuous for all values of x. (Hint: Using the definition of the absolute value function, compute .limx →0^-|x| and limx →0^ |x| .)
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(a) Show that the absolute value function F(x) = | x | is continuous everywhere. (b) Prove that if f is a continuous function on an interval, then so is | f | . (c) Is the converse of the statement in part (b) also true? In other words, if | f | is continuous, does it follow that f is continuous? If so, prove it. If not, find a counterexample. | Numerade
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