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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
Show that 571 is a prime number. Ans: Let x=571⇒√x=√571 Now 571 lies between the perfect squares of (23)2 and (24)2 Prime numbers less than 24 are 2,3,5,7,11,13,17,1
what is the difference between North America''s part of the total population and Africa''s part
Given, y = f(x) = 2 x 3 - 3x 2 + 4x +5 a) Use the Power function to find derivative of the function. b) Find the value of the derivative at x = 4.
(a) Assume that A is a m 1 ×m 2 matrix and B is a m 2 ×m 3 matrix. How many multiplications are required to calculate the matrix product AB? (b) Given that A 1 is a 20 × 50 m
If the points (5, 4) and (x, y) are equidistant from the point (4, 5), prove that x 2 + y 2 - 8x - 10y +39 = 0. Ans : AP = PB AP 2 = PB 2 (5 - 4) 2 + (4 - 5) 2 = (x
The positive value of k for which x 2 +Kx +64 = 0 & x 2 - 8x + k = 0 will have real roots . Ans: x 2 + K x + 64 = 0 ⇒ b 2 -4ac > 0 K 2 - 256 > 0 K
how much is this
3.6 in a fraction
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Determine the second derivative for following functions. Q (t ) = sec (5t ) Solution : Following is the first derivative. Q′ (t
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