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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
A man invests rs.10400 in 6%shares at rs.104 and rs.11440 in 10.4% shares at rs.143.How much income would he get in all?
Two circles C(O, r) and C 1 (O 1 , r 1 ) touch each other at P, externally or internally. Construction: join OP and O 1 P . Proof : we know that if two circles touch each
Find the equation of the plane through (2, 1, 0) and parallel to x + 4y 3z = 1.
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
A solid is formed by cutting the top off of a cone with a slice parallel to the base, and then cutting a cylindrical hole into the resulting solid. Determine the volume of the holl
Draw the direction field for the subsequent differential equation. Draw the set of integral curves for this differential equation. Solution: y′ = y - x To draw direct
Finite Population Correction Factor Or Fpcf) If a specified population is relatively of small size and sample size is more than 5 percent of the population then the standard er
a drawn picture on a graph that includes equations of each line
One integer is two more than another. The sum of the lesser integer and double the greater is 7. What is the greater integer? Let x = the greater integer and y = the lesser int
Q. Addition Involving Negative Numbers? Ans. When you add together positive and negative numbers, there are essentially three possibilities that you can encounter. Let's e
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