SOLVED:Given a continuous function f on an interval I, prove-using ordinary integration of functions - that there exists a unit-speed curve β(s) in 𝐑^2 for which f(s) is the plane curvature. (Hint: Reverse the logic in Ex. 8 of Sec. 2.3.)
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SOLVED:(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|1 (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.
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