By C. B. Gupta

ISBN-10: 8122426859

ISBN-13: 9788122426854

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**Example text**

2x(3) + 3x(2) + 2x(1) – 10, 6x(2) + 6x(1) + 2, 12x + 6, 12 17. 1 (4) 9 (2) x + 2x(3) + x + 12x(1) + C 4 2 18. (i) (iv) ex +C (e h − 1) x ( 3) 5 x ( 2 ) + +C 3 2 (ii) x ( 3) +C 3 (iii) ax + C (v) – 1 sin x 2 (vi) 1 x 5. , xn respectively, then the method to obtaining the value of f (x) at point x = xi which lie between x0 and xn is called interpolation. Thus, interpolation is the technique of computing the value of the function outside the given interval. If x = xi does not lie between x0 and xn then computing the value of f (x) at this point is called the extra polation.

Bm 2 x 2 + ...... + bmn x n = bm′ Assuming a11 ≠ 0. The variable x1 eliminated from second equation by subtracting U| || V| || W Step 2. To eliminate x2 from the third, fourth ...... nth equation Assuming b22 ≠ 0. The variable x2 eliminated from third equation by subtracting b32 times the b22 second equation from the third equation, similarly we eliminate x2 from fourth equation by subtracting b42 times the second equation from the fourth equation etc. We get new system of equation as b22 44 ADVANCECED MATHEMATICS U| || V| | = b ′′ |W a11 x1 + a12 x 2 + a13 x 3 + ......

Bmn x n = bm′ Assuming a11 ≠ 0. The variable x1 eliminated from second equation by subtracting U| || V| || W Step 2. To eliminate x2 from the third, fourth ...... nth equation Assuming b22 ≠ 0. The variable x2 eliminated from third equation by subtracting b32 times the b22 second equation from the third equation, similarly we eliminate x2 from fourth equation by subtracting b42 times the second equation from the fourth equation etc. We get new system of equation as b22 44 ADVANCECED MATHEMATICS U| || V| | = b ′′ |W a11 x1 + a12 x 2 + a13 x 3 + ......

### Advanced Mathematics by C. B. Gupta

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