# 1. Obtain the estimate of the missing figure in the following table. X 2 2.1 2.2 2.3 2.4 2.5 2.6 Y 0.135 - 0.111 0.100 - 0.082 0.074 2. Using the lagrenges formula find the form of the function f(x) given that x 0 2 3 6 f(x) 659 705 729 804

Jitender Singh IIT Delhi
8 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 1stcase 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