Last night you had the strangest dream Among other things, a guy named Dirac appeared in your dreams, and he started talking about the importance of the Heaviside function The Heaviside function, denoted by H(x), is given by H(x) 0 if 10 x 0 if 0 x 10 a) Use the FTC to prove that the following statement is false there exists a continuous function f on 10, 10 such that H(x) f(t)dt b) Let us see what happens when we allow ourselves to choose f from a larger class of functions Decide whether the following statement is true or false, and prove it or disprove it accordingly there exists a bounded function f, integrable on 10, 10 such that H(x) f(t)dt

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Last night you had the strangest dream. Among other things, a guy named Dirac appeared in your dreams, and he started talking about the

Last night you had the strangest dream. Among other things, a guy named Dirac appeared in your dreams, and he started talking about the importance of the Heaviside function. The Heaviside function, denoted by H(x), is given by H(x) = == {{ 0 if 10 x 0 if 0 < x

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