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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
Solve the fractional equation: Example: Solve the fractional equation 1/(x-2) +1/(x+3) =0 Solution: The LCD is (x - 2)(x + 3); therefore, multiply both sides of t
for all real numbers x, x 0
Find out where the following function is increasing & decreasing. A (t ) = 27t 5 - 45t 4 -130t 3 + 150 Solution As with the first problem first we need to take the
Examples of logarithms: log 2 8 = 3 since 8 = 2 3 log 10 0.01 = -2 since 0.01 = 10
Differentiate following functions. g ( x ) = 3sec ( x ) -10 cot ( x ) Solution : There actually isn't a whole lot to this problem. We'll just differentia
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
#subtraction of binary numbers methods
x^2-5x+4 can written in roots as (x-1)*(x-4) x^2-4 can be written interms of (x-2)(x+2).so [(x-1)(x-4)/(x-2)(x+2)]
Variance Consider the example of investment opportunities. The expected gains were Rs.114 and Rs.81 respectively. The fact is that an investor also looks at the dispersion befo
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