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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
If the p th , q th & r th term of an AP is x, y and z respectively, show that x(q-r) + y(r-p) + z(p-q) = 0 Ans: p th term ⇒ x = A + (p-1) D q th term ⇒ y = A + (
What inequalities and intervals are? If it is given that a real number 'p' is not less than another real number 'q', we understand that either p should be equal to q or
Determine and classify all the critical points of the given function. Described the intervals where function is increasing & decreasing. Solution: Firstly we'll require
Kenny used a micrometer to measure the thickness of a piece of construction paper. The paper measured halfway among 0.24 millimeters and 0.25 millimeters. What is the thickness of
A car travels at a rate of (4x2 - 2). What is the distance this car will travel in (3x - 8) hours? Use the formula distance = rate × time. Through substitution, distance = (4x2
mentioning the type of business you could start and the location of your business, use the steps of quantitative methods for decision making narrating them one by one in the applic
Express the GCD of 48 and 18 as a linear combination. (Ans: Not unique) A=bq+r, where o ≤ r 48=18x2+12 18=12x1+6 12=6x2+0 ∴ HCF (18,48) = 6 now 6
find the diameter of circle whose circumference is 26.51
Trig Substitutions - Integration techniques As we have completed in the last couple of sections, now let's start off with a couple of integrals that we should previously be
The points A,B,C and D represent the numbers Z1,Z2,Z3 and Z4.ABCD is rhombus;AC=2BD.if Z2=2+i ,Z4=1-2i,find Z1 and Z3 Ans) POI of diagonals: (3-i)/2. Using concept of rotation:
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