Applied Mathematics for Electrical Engineering (3130908)

Question-2a

BE | Semester-3 Winter-2019 | 26-11-2019

Q2) (a)

If $f (x) = \frac{1}{x}$ , prepare the table for finite differences and hence find $[a, b]$ and $[a, b, c]$ .

$[a, b] = \frac{f (b) - f (a)}{b - a}$

$[a, b] = \frac{\frac{1}{b} - \frac{1}{a}}{b - a}$

$[a, b] = \frac{a - b}{a b (b - a)}$

$[a, b] = \frac{- (b - a)}{a b (b - a)}$

$[a, b] = - \frac{1}{a b}$

$[a, b, c] = \frac{[b, c] - [a, b]}{c - a}$

$[a, b, c] = \frac{(- \frac{1}{b c}) - (- \frac{1}{a b})}{c - a}$

$[a, b, c] = \frac{- a b + b c}{a b^{2} c (c - a)}$

$[a, b, c] = \frac{b (c - a)}{a b^{2} c (c - a)}$

$[a, b, c] = \frac{1}{a b c}$

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