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All the integrals below are understood in the sense of the Lebesgue.
(1) Prove the following equality which we used in class without proof. As-sume that f integrable over [3; 3]. Then
(2) Assume that f is integrable over [0; 1]. Show that
is di erentiable a.e on (0; 1).
(3) Assume that f is continuous on [0; 1]. Suppose that
Lucy's Lunch is sending out flyers and pays a bulk rate of 14.9 cents per piece of mail. If she mails 1,500 flyers, what will she pay? Multiply the price per piece through the
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Illustration : Solve the following IVP. Solution: First get the eigenvalues for the system. = l 2 - 10 l+ 25 = (l- 5) 2 l 1,2 = 5 Therefore, we got a
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Question Solve the following functions for x (where x is a real number). Leave your answers in exact form, that is, do not use a calculator, show all working. (a) 3 x 3 x2 3
Submit your working in (neat) handwritten form (do not type up your solutions). For the plots that you generate in Maple or Matlab, you can print them out and attach them at the en
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Important formulas d (a b )/ dx = 0 This is a constant d ( x n ) / dx = nx n -1 Power Rule d (a x ) / dx = a x l
write in factor form 9x3+9x5
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