2. (a) The coordinates, (xy), of points on the curve y = fx) are given in the lable below. 3. 4 16 1. 4. Use Simpson's rule to estimate (0) (i) the area enclosed between the curve, the x axis and the ordinate at x4. the volume of the solid obtained when the arca in (i) is rotated complesely ahoul the x-axis. Oltaiu die Taylın seuics capansion of y-Ra) about a - Hence, or otherwise, show that if (xy,). (x,.). (x,1) are successive point of curve y =Ax), such that x-X= Xe- X=h then (0) dx (i) Y y +2h (ii) (c) Given that y satisfics the differential cqualion (x+1) = 2x - y, de dy usc the approximation y.."y. + with A-0.2 to find the value of y when x-0.4 given that y1 when x0. (Give your anawer to 3 sigailicaat ligures).
Permutations and Combinations
If there are 5 dishes, they can be relished in any order at a time. In permutation, it should be in a particular order. In combination, the order does not matter. Take 3 letters a, b, and c. The possible ways of pairing any two letters are ab, bc, ac, ba, cb and ca. It is in a particular order. So, this can be called the permutation of a, b, and c. But if the order does not matter then ab is the same as ba. Similarly, bc is the same as cb and ac is the same as ca. Here the list has ab, bc, and ac alone. This can be called the combination of a, b, and c.
Counting Theory
The fundamental counting principle is a rule that is used to count the total number of possible outcomes in a given situation.
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