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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
Download the data on Gas Mileage. This is a sample of 81 passenger cars with information about gas consumption and other technical details. a. Estimate the following
64% of the students within the school play are boys. If there are 75 students in the play, how many are boys? To ?nd out 64% of 75, multiply 75 by the decimal equivalent of 64%
Wendy has 5 pairs of pants and 8 shirts. How many different combinations could she form with these items? Multiply the number of choices for each item to find out the number of
show that a*0=a
Example1 : Solve the subsequent system of equations. -2x 1 + x 2 - x 3 = 4 x 1 + 2x 2 + 3x 3 = 13 3x 1 + x 3 = -1 Solution The initial step is to write d
Perform the denoted operation for each of the following. (a) Add 6x 5 -10x 2 + x - 45 to 13x 2 - 9 x + 4 . (b) Subtract 5x 3 - 9 x 2 + x - 3 from x 2+ x +1.
Which of the subsequent numbers will yield a number larger than 23.4 while it is multiplied by 23.4? When multiplying through a number less than 1, you get a product in which i
By the method of completion of squares show that the equation 4x 2 +3x +5 = 0 has no real roots. Ans: 4 x 2 +3 x +5=0 ⇒ x 2 + 3/4 x + 5 = 0 ⇒ x 2 + 3/4 x +
together, pearl and harvey are going to visit their aunt on sunday. If Pearl visits their aunt every 6 days, while harvey every 8 days, on what day will they visit their aunt toget
A rescue and ?re squad places a 15 ft ladder against a burning building. If the ladder is 9 ft from the base of the building, how far up the building will the ladder reach? a. 8
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