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Numerical Methods - Miscellaneous Problems | 12th Business Maths and Statistics : Chapter 5 : Numerical Methods

Chapter: 12th Business Maths and Statistics : Chapter 5 : Numerical Methods

Miscellaneous Problems

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Miscellaneous Problems

1. If f ( x) = eax then show that f ( 0), Δ f ( 0), Δ2 f ( 0) are in G.P



2. Prove that i) ( 1 + Δ )( 1 - ) = 1 ii) Δ ∇ = Δ −  (iii) E  = Δ  = E



3. A second degree polynomial passes though the point (1,-1) (2,-1) (3,1) (4,5). Find the polynomial.



4. Find the missing figures in the following table




5. Find f ( 0.5) if f ( −1) = 202, f ( 0) = 175 , f (1) = 82 and f ( 2) = 55



6. From the following data find y at x = 43 and x = 84




7. The area A of circle of diameter ‘d’ is given for the following values


Find the approximate values for the areas of circles of diameter 82 and 91 respectively.




8. If u0 = 560, u1 = 556, u2 = 520, u4 = 385, show that u3 = 465



9. From the following table obtain a polynomial of degree y in x





10. Using Lagrange’s interpolation formula find a polynomial which passes through the points (0, –12), (1, 0), (3, 6) and (4,12).




Answers:


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