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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
which one of the following examples represents a repeating decimal? 0.123123,1.111114,0.777777,4.252525?
Find out the next number in the subsequent pattern. 320, 160, 80, 40, . . . Each number is divided by 2 to find out the next number; 40 ÷ 2 = 20. Twenty is the next number.
MAKING CONNECTIONS : you have read about what the ability to think mathematically involves. In this section we shall discuss ways of developing this ability in children. As yo
Maria has a slice of pizza that is1/6 the pizza. Ben has a slice of pizza that is 1/3 of the pizza . Maria''s slice is bigger .draw pizzas to show how this possible .
y 2 = t 2 - 3 is the actual implicit solution to y'= t/y, y(2) = -1. At such point I will ask that you trust me that it is actually a solution to the differential equation. You w
briefly explain how the famous equation for the loss of heat in a cylindrical pipe is derived
Explain Adding Negative Fraction? To add negative fractions: 1. Find a common denominator. 2. Change the fractions to their equivalents, so that they have common denominators
The sum of the diameters of two circles is 2.8 m and their difference of circumferences is 0.88m. Find the radii of the two circles (Ans: 77, 63) Ans: d 1 + d 2 = 2.8 m=
what are integars
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 +
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