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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
Q. What is Uniform Distribution? Ans. A distribution is the set of possible values of a random variable considered in terms of their theoretical or observed frequency. Th
A class has 175 learners. The given table describes the number of learners studying one or more of the subsequent subjects in this case Subjects
A 4-inch by 6-inch photograph is going to be enlarged through increasing each side by the similar amount. The new area is 168 square inches. How many inches is each dimension incre
Multiply following and write the answers in standard form. (a) 7 i ( -5 + 2 i ) (b) (1 - 5 i ) ( -9 + 2 i ) Solution (a) Thus all that we have to do is distribu
Calculate log equation: Calculate log 10 2 - log 10 3. Solution: Rule 2. log 10 (A/B): log 10 A - log 10 B log 10 2 - log 10 3 = log 10 (2/3) =
THINKING MATHEMATICALLY : Have you ever thought of what mental processes you are going through when you are solving a mathematical problem? Why don't you try the following proble
what is the value of integration limit n-> infinity [n!/n to the power n]to the power 1/n Solution) limit n-->inf. [1 + (n!-n^n)/n^n]^1/n = e^ limit n-->inf. {(n!-n^n)
Evaluate the area of the region. a. 478 units 2 b. 578 units 2 c. 528 units 2 d. 428 units 2 b. Refer to the diagram to evaluate the area of the shaded
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The last topic that we have to discuss in this section is that of parallel & perpendicular lines. Following is a sketch of parallel and perpendicular lines. Suppose that th
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