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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 dierentiable a.e on (0; 1).
(3) Assume that f is continuous on [0; 1]. Suppose that
Show that the product of 3 consecutive positive integers is divisible by 6. Ans: n,n+1,n+2 be three consecutive positive integers We know that n is of the form 3q, 3q +1
Suppose you are in the market for a new home and are interested in a new housing community under construction in a another city. a) The sales representative later shows that there
Variation of Parameters Notice there the differential equation, y′′ + q (t) y′ + r (t) y = g (t) Suppose that y 1 (t) and y 2 (t) are a fundamental set of solutions for
Determine how many different words can be formed out of the letters of the word VARANASI? Ans: 720 different words can be formed out of the letters of the word VARANASI.
Example of division of fractions: Example: (4/5)/(2/9) = Solution: Step 1: Invert the divisor fraction (2/9) to (9/2). Step 2: Multip
what is the basic unit of weight in the metric system?
Special Forms There are a number of nice special forms of some polynomials which can make factoring easier for us on occasion. Following are the special forms. a 2 + 2ab +
Regression - Measures of Relationships - It is a concept that refers to the changes which happen in the dependent variable as a result of changes happens on the independent va
When three quantities a, b and c are in G.P., then the geometric mean "b" is calculated as follows. Since these quantities are in G.P., the r
A police academy is training 14 new recruits. Some are working dogs and others are police officers. There are 38 legs in all. How many of each type of recruits are there?
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