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Integral Calculus> Interpolation...

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1. Obtain the estimate of the missing figure in the following table.X22.12.22.32.42.52.6Y0.135-0.1110.100-0.0820.0742. Using the lagrenges formula find the form of the function f(x) given thatx0236f(x)659705729804

anitha ashok , 13 Years ago

Grade Upto college level

1 Answers

Jitender Singh

Last Activity: 10 Years ago

Ans:

2.

Using the langrange formula, we have

$f(x) = \frac{(x-x_{2})(x-x_{3})(x-x_{6})}{(x_{0}-x_{2})(x_{0}-x_{3})(x_{0}-x_{6})}f(0)+\frac{(x-x_{0})(x-x_{3})(x-x_{6})}{(x_{2}-x_{0})(x_{2}-x_{3})(x_{2}-x_{6})}f(2)$ $+\frac{(x-x_{2})(x-x_{0})(x-x_{6})}{(x_{3}-x_{0})(x_{3}-x_{2})(x_{3}-x_{6})}f(3)+\frac{(x-x_{2})(x-x_{3})(x-x_{0})}{(x_{6}-x_{0})(x_{6}-x_{2})(x_{6}-x_{3})}f(6)$

$f(x) = \frac{(x-2)(x-3)(x-6)}{(0-2)(0-3)(0-6)}.659+\frac{(x-0)(x-3)(x-6)}{(2-0)(2-3)(2-6)}.705$

$+\frac{(x-2)(x-0)(x-6)}{(3-0)(3-2)(3-6)}.729+\frac{(x-2)(x-3)(x-0)}{(6-0)(6-2)(6-3)}.804$

$f(x) = \frac{(x-2)(x-3)(x-6)}{-36}.659+\frac{(x-0)(x-3)(x-6)}{-8}.705$

$+\frac{(x-2)(x-0)(x-6)}{-9}.729+\frac{(x-2)(x-3)(x-0)}{72}.804$

Similarly, you can find the f(x) in the 1^stcase from the given values, & then you you can easily find the value of f(2.1) & f(2.4)

Thanks & Regards

Jitender Singh

IIT Delhi

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