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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
Are the two angles of a rectangles congruent ? why ?
How do i add 4+2
Minima, Maxima and points of inflexion a) Test for relative maximum Consider the given function of x whose graph is presented by the figure given below
1. How many closed necklaces of length 7 can be made with 3 colors? (notice that 7 is a prime) 2. How many closed necklaces of length 10 can be made with 3 colors (this is di erent
zeroes of polynomial 2x2-3x-2
Question: There are 6 letters and 6 self addressed envelopes.What is the probability that atleast 1 is placed correctly?? Ans: If we let A be the event that letter A is in the cor
If the normal to y=f(x) makes an angle of pie/4 with y-axis at (1,1) , then f''(x) is eqivalent to? Ans) The normal makes an angle 135 degree with the x axis. also f ''(1)
what is the difference between North America''s part of the total population and Africa''s part
Optimization : In this section we will learn optimization problems. In optimization problems we will see for the largest value or the smallest value which a function can take.
Urn A contains 1 white,2 black and 3 red balls;Urn B contains 2 white,1 black and 1 red balls;and Urn C contains 4 white,5 black and 3 red balls.One urn is chosen at random and two
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