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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
What do you need to multiply 30 by to get 1500? This will give you the top edge length of the rectangle. Can you then figure out what must go below the 30 in order to get the area
1.If a+b=2b and ab+cd+ad=3bc,prove that a,b,c,d are in A.P 2.The nth term of an A.P is an+b.Find the sum of the series upto n terms.
Chi Square Distribution Chi square was first utilized by Karl Pearson in 1900. It is denoted by the Greek letter χ 2 . This contains only one parameter, called the number of d
A chemist has one solution which is 50% acid and a second which is 25% acid. How much of each should be mixed to make 10 litres of 40% acid solution.
Evaluate following limits. Solution In this part what we have to note (using Fact 2 above) is that in the limit the exponent of the exponential does this, Henc
Example of Product moment correlation The given data was acquired during a social survey conducted in a described urban area regarding the yearly income of described families
Given f (x) = - x 2 + 6 x -11 determine each of the following. (a) f ( 2) (b) f ( -10) (c) f (t ) Solution (a) f ( 2) = - ( 2) 2 + 6(2) -11 = -3 (
what is the difference between North America''s part of the total population and Africa''s part
Q. Illustrate Pythagorean Theorem? Ans. You have definitely seen the Pythagorean Theorem before, so a 2 + b 2 = c 2 should look familiar to you. The Pythagorean Theor
Cone - Three dimensional spaces The below equation is the general equation of a cone. X 2 / a 2 + y 2 /b 2 = z 2 /c 2 Here is a diagram of a typical cone. Not
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