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Using differentials, find the approximate value of ` sqrt(0.037)`. |
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Answer» Let y = `sqrtx` Let x =0.04 and ` x+ Deltax = 0.037` ltbr. `rArr 0.04 + Deltax = 0.037` ` rArr Deltax =- 0.003` At x = 0.04, ` y= sqrt(0.04) = 0.2` Now `y=sqrtx` `rArr (dy)/(dx) = 1/(2sqrtx)` At x= 0.04, ` (dy)/(dx) = 1/(2sqrt(0.04))= 1/(0.4) = 2.5` `:. Deltay = (dy)/(dx) . Deltax = 2.5 xx (-0.003) =- 0.0075` and ` y+ Deltay = 0.2 - 0.0075` ` rArr sqrt(0).037 = 0.1925`. |
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