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Using differentials, find the approximate value of `root(3)127`. |
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Answer» Let `y = root(3)x = x^(1//3)` Let x = 125 and x + ` Deltax = 127` ` rArr Deltax = 2` ` At x = 125` `y = root(3)125 =5` Now `y= x^(1//3)` `rArr (dy)/(dx) = 1/3 x^(-2//3) = 1/ (3x^(2//3))` At x = 125, ` (dy)/(dx) = 1/(3(125)^(2//3)) = 1/75` `:. Delta y = (dy)/(dx) . Deltax = 1/75 xx 2 = 2/75 = 0.026` ` and y+Deltay = 5 + 0.026` ` rArr (127)^(1//3)= 5.026`. |
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