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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
When 6 boys were admitted & 6 girls left the percentage of boys increased from 60% to 75%. Find the original no. of boys and girls in the class. Ans: Let the no. of Boys be x
Determine Rank Correlation Coefficient A group of 8 accountancy students are tested in Quantitative Techniques and Law II. Their rankings in the two tests were as:
Suppose that we know the logarithms of all numbers which are expressed to base 'a' and we are required to find the logarithms of all these numbers to base 'b'. We
20% of $19.95
Nancy, Jennifer, Alex, and Joy ran a race. Nancy's time was 50.24 seconds, Jennifer's was 50.32, Alex's was 50.9, and Joy's was 50.2. Whose time was the fastest? The fastest ti
PROBLEMS WITH APPLYING ALGORITHMS : From your experience, you would agree that children are expected to mechanically apply the algorithms for adding or subtracting numbers, regar
A teacher on attempting to arrange the students for mass drill in the form of a solid square found that 24 students were left over. When he increased the size of the square by one
apzza driver delivered 27 pizzas in one night he delivered more then one pizza to only one house . every other hhouse he only delivered pizza to 18 houses . how many pizzas did he
If y 1 (t) and y 2 (t) are two solutions to y′′ + p (t ) y′ + q (t ) y = 0 So the Wronskian of the two solutions is, W(y 1 ,y 2 )(t) = =
Logarithmic Differentiation : There is one final topic to discuss in this section. Taking derivatives of some complicated functions can be simplified by using logarithms. It i
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