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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
to which subset of the real number does the number 22 belong?
Ten is decreased through four times the quantity of eight minus three. One is then added to in which result. What is the final answer? The area of a square whose side measures
Find the lesser of two consecutive positive even integers whose product is 168. Let x = the lesser even integer and let x + 2 = the greater even integer. Because product is a k
We know that the terms in G.P. are: a, ar, ar 2 , ar 3 , ar 4 , ................, ar n-1 Let s be the sum of these terms, then s = a + ar + ar 2
Finds out the center & radius of each of the following circles & sketch the graph of the circle. a) x 2 + y 2 = 1 b) x 2 + ( y - 3) 2 = 4 Solution In all of these
Draw a flowchart for accumulated principal at the end of 5 years by taking into account compound interest?
Geometric Applications to the Cross Product There are a so many geometric applications to the cross product also. Assume we have three vectors a → , b → and c → and we make
? (2x+3)dx
The length of the sides of a triangle are 2x + y/2 , 5 x/3 + y + 1/2 and 2/3 x + 2y + 5/2. If the triangle is equilateral. Find its perimeter. A ns: 2x + y/2 = 4x + y
Question: Find the quotient and remainder when f(x) = x 5 - x 4 - 4x 3 + 2x + 3 is divided by g(x) = x-2. Make sure the quotient and remainder are clearly identified.
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