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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
1. Suppose n ≡ 7 (mod 8). Show that n ≠ x 2 + y 2 + z 2 for any x, y, z ε Z. 2. Prove ∀n ε Z, that n is divisible by 9 if and only if the sum of its digits is divisible by 9.
What is Permutations explain with examples? Each arrangement of a set of elements is called a permutation. In other words, every possible way (order) of writing a group of lett
It is a fairly short section. It's real purpose is to acknowledge that the exponent properties work for any exponent. We've already used them on integer and rational exponents al
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Solve 4 sin 2 ( t ) - 3 sin ( t /3)= 1 . Solution Before solving this equation let's solve clearly unrelated equation. 4x 2 - 3x = 1 ⇒ 4x 2 - 3x -1 = ( 4x + 1) ( x
Kelli calls her grandmother every month Kelli also calls her cousin.If Kelli calls her cousin in January, how many calls will Kelli have made to her grandmother and her cousin by t
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how do i multiply demencinals
From a point P, two tangents PA are drawn to a circle with center O.If OP=diameter of the circle show that triangle APB is equilateral. Ans: PA=PB (length of tangents
Determine the second derivative for following functions. Q (t ) = sec (5t ) Solution : Following is the first derivative. Q′ (t
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