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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
Martha has $20 to spend and would like to buy as several calculators as possible along with the money. The calculators that she needs to buy are $4.50 each. How much money will she
(b) The arity of an operator in propositional logic is the number of propositional variables that it acts on – for example, binary operations (e.g, AND, OR, XOR…) act on two propo
Refer the poset ({1}, {2}, {4}, {1,2}, {1,4}, {2,4}, {3,4}, {1,3,4}, {2,3,4}, ≤ ). (i) Find out the maximal elements. (ii) Find out the minimal elements. (iii) Is ther
Theory of Meta-games This theory shows to describe how most people play non zero sum games concerning a number of persons Prisoner's dilemma is an illustration of this. The
The graph C n , n ≥ 3 contains n vertices and n edges creating a cycle. For what value of n is C n a bipartite graph? Draw the bipartite graph of C n to give explanation for yo
Find the derivatives of the following functions a) y = 5x 4 +3x -1-x 3 b) y = (x+1) -1/2 c) y= e x2+1 d) y= e 3x lnx e) y =ln(x+1/x)y
nc6:n-3c3=91:4
Mean Value Theorem : Suppose f (x) is a function which satisfies both of the following. 1. f ( x )is continuous on the closed interval [a,b]. 2. f ( x ) is differentiable on
13 1/4 34 56/89
1.) How does the monsoon influence the climate and vegetation of Southeast Asia? 2.) What is the main crop in Southeast Asia and the main systems by which it is produce? How and
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