 # Finite difference

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Published on February 27, 2014

Author: ManishJaiswal12

Source: slideshare.net

Assignment#1 Finite Difference & Interpolation 1.Find the polynomial f(x) , which satisfy the following data and hence find the value of f(1.5). X 1 2 3 4 5 F(X) 4 13 34 73 136 2.Evaluate the missing terms in the following table: X 0 1 2 3 4 5 F(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 1997 Production f(x) 20 23 26 29 ----34 45 3 6. Prove that ∆ (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 +12 9. Compute (i) f(1.38) and (ii) f(1.42) from the table : X 1.1 1.2 1.3 1.4 F(X) 7.831 8.728 9.697 10.744 10. 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 80-99 No. of candidates 41 62 65 50 17 Estimate the numbers of candidates getting marks less than 70. 11. Compute f(5) from the given data: X 2 4 7 9 F(X) 10 26 65 101 12. Use Newtion’s divided difference formula to find (i) f(8) and (ii) f(15) from the table: X 4 5 7 10 11 13 F(X) 48 100 294 900 1210 2078 13. Find the polynomial of the least degree, which attains the prescribed values at the given points: X -2 1 2 4 F(X) 25 -8 -15 -25 14. Compute the value of x, for y= 0.6742 from the table X 3.5 4 4.8 5.6 Y 0.5441 0.602 0.6812 0.7482 0 .

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