the area enclosed between the curve, the x axis and the ordiaate at x4. the volume of the solid obtained when the arca in (i) is rotated compleiely ahout the X-axis.
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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Answer Q2a
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(a)
The coordinates, (x), of points on the curve y = ffx) are given in the table below.
2.
3.
4
1.
4.
16
Use Simpson's rule to estimate
(i)
(ii)
the area enclosed between the curve, the x axis and the ordinate at x 4.
the volume of the solid obtained when the arca in (i) is retated completely ahout the
X- axis.
Oltaiu die Taylu scics capasion of y -a aloutx-An
Hence, or otherwise, show that if (xy). (x.,.). (x. ) arc successive point on the
()
curve y =x), such that Xn-X-=Xn+- X= h then
dy
Va * V. +
dx
(0)
dy
Ya * V+ 2h
de),
(i1)
(d'y
(ii)
(c)
Given that y satisfies the differential equation (x+1) = 2x - y,
dx
dy
usc the approximation y" y, +
dx
with A = 0.2 to find the value of y when.r- 0.4 given that y=1 when x= 0.
(Give your anawer to 3 signilicant ligurcs)."
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