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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
Consider the function f(x) =1/2 (2 x +2 -x ) which has the graph (a) Explain why f has no inverse function. You should include an example to support your explanation
Determine if the following sequences are monotonic and/or bounded. (a) {-n 2 } ∞ n=0 (b) {( -1) n+1 } ∞ n=1 (c) {2/n 2 } ∞ n=5 Solution {-n 2 } ∞ n=0
Analysis of questionnaire completed by holiday makers showed that 0.75 classified their holiday as excellent at Malindi. The probability of hot weather in the resort is 0.6. If th
Calculate the mean, variance & standard deviation of the number of heads in a simultaneous toss of three coins. SOLUTION: Let X denotes the number of heads in a simu
16 times 4
two fathers and two sons went fishing . they caught only 3 fish and divided them equally among themselves without cutting. is it possible? how?
[ ] meaning
Give an examples of Simplifying Fractions ? When a fraction cannot be reduced any further, the fraction is in its simplest form. To reduce a fraction to its simplest form,
Let {An} be sequence of real numbers. Define a set S by: S={i ? N : for all j > i, ai
The perimeter of a rectangle is 21 inches. What is the measure of its width if its length is 3 inches greater than its width? Let x = the width of the rectangle. Let x + 3 = th
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