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The Cartesian product (also called as the cross product) of two sets A and B, shown by AΧB (in the similar order) is the set of all ordered pairs (x, y) such that x€A and y€B. What we indicate by ordered pair is that the pair (a, b) is not the same pair as (b, a) unless a = b. It implies that AΧB ≠ BΧA in common. Also if A contains m kind of elements and B contains n elements then AΧB have mΧn elements.
Same as we may define AΧA = {(x, y); x€A and y€A}. We may also define cartesian product of more than two sets.
Find the number of square feet of pavement required for the shaded portion of the streets shown in the figure, all the streets being 50 feet wide.
Evaluate following integrals. (a) ∫ 3e x + 5 cos x -10 sec 2 x dx (b) ( 23/ (y 2 + 1) + 6 csc y cot y + 9/ y dy Solution (a) ∫ 3e x + 5 cos x -10 sec 2 x
Find out if each of the subsequent series are absolute convergent, conditionally convergent or divergent. Solution: (a) The above is the alternating harmonic ser
what are the applications of de moiver''s theorem in programming and software engineering
Rationalize the denominator for following. Suppose that x is positive. Solution We'll have to start this one off along with first using the third property of radica
Here we will use the expansion method Firstly lim x-0 log a (1+x)/x firstly using log property we get: lim x-0 log a (1+x)-logx then we change the base of log i.e lim x-0 {l
If two zeros of the polynomial f(x) = x 4 - 6x 3 - 26x 2 + 138x - 35 are 2 ± √3.Find the other zeros. (Ans:7, -5) Ans : Let the two zeros are 2 +√3 and 2 - √3 Sum of
There may be more than one independent variable which determines the value of y. The dimension of a function is determined by the number of independent variables in the
Marvin is helping his teachers plan a ?eld trip. There are 125 people going on the ?eld trip and each school bus holds 48 people. What is the minimum number of school buses they wi
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