Assignment#1

Finite Difference & Interpolation1.Find the polynomial f(x) , which satisfy the following data and hence find the value of f(1.5).

X 1 2 3 4 5F(X) 4 13 34 73 136

2.Evaluate the missing terms in the following table:

X 0 1 2 3 4 5F(X) 0 -- 8 15 -- 35

3. Find the first term of the series whose second and subsequent terms are 8, 3, 0, -1, 0,…. 4. Evaluate (∆2/E) x3 .5.Estimate the production of cotton in the year 1995 from the data given below:Year (x) 1991 1992 1993 1994 1995 1996 1997Production f(x) 20 23 26 29 ----- 34 456. Prove that ∆3 (1-x)(1-2x)(1-3x) = -36, interval of differencing being unity.7. Express the following functions in their factorial notation, taking h=1. (a) f(x)= 2x3 – 3x2 +3x –10 (b) f(x) = x4 –12x3 + 12x2 –30x +9.8. Find the functions, where first differences are

(a) 9x2 +11x +5 (b) x3 +3x2 +5x +129. Compute (i) f(1.38) and (ii) f(1.42) from the table : X 1.1 1.2 1.3 1.4F(X) 7.831 8.728 9.697 10.74410. In an examination the number of candidates who secured marks between certain limits were as follows:Marks 0-19 20-39 40-59 60-79 80-99No. of candidates 41 62 65 50 17Estimate the numbers of candidates getting marks less than 70.11. Compute f(5) from the given data:X 2 4 7 9F(X) 10 26 65 10112. Use Newtion’s divided difference formula to find (i) f(8) and (ii) f(15) from the table:X 4 5 7 10 11 13F(X) 48 100 294 900 1210 207813. Find the polynomial of the least degree, which attains the prescribed values at the given points:X -2 1 2 4F(X) 25 -8 -15 -2514. Compute the value of x, for y= 0.6742 from the tableX 3.5 4 4.8 5.6Y 0.5441 0.602

00.6812 0.7482

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