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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
solution of properties of definite integral
Q. Show Inverse Trigonometric Functions? Ans. Many functions, including trig functions, are invertible. The inverse of trig functions are called ‘inverse trig functions'.
Relations in a Set: Let consider R be a relation from A to B. If B = A, then R is known as a relation in A. Thus relation in a set A is a subset of A ΧA. Identity Relation:
( 1/2)2 x 1/5+1/6=
(p:4:3p
even numbers
Quotient Rule : If the two functions f(x) & g(x) are differentiable (that means the derivative exist) then the quotient is differentiable and,
Q. Define natural numbers Ans. The natural numbers (also called the counting numbers) are the numbers that you "naturally" use for counting: 1,2,3,4,... The set of n
1,5,14,30,55 find the next three numbers and the rule
It is the simplest case which we can consider. Unforced or free vibrations sense that F(t) = 0 and undamped vibrations implies that g = 0. Under this case the differential equation
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