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If `y = 1 +(1)/(x) +(1)/(x^(2)) + (1)/(x^(3)) + ……..+oo` with `|x| gt 1` then `(dy)/(dx)` is .A. `(x^(2))/(y^(2))`B. `x^(2)y^(2)`C. `(y^(2))/(x^(2))`D. `-(y^(2))/(x^(2))` |
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Answer» Correct Answer - D Given ` y = 1 +(1)/(x^(1)) +(1)/(x^(2)) +(1)/(x^(3))..........oo` `rArr " "y = (1)/(1-(1)/(x)) = (x)/(x-1)` On differentianting , we get `(dy)/(dx) = ((x-1)-x)/((x-1)^(2)) = (1)/((x-1)^(2))` `rArr (dy)/(dx) = -((y)/(x))^(2) = -(y^(2))/(x^(2))" "[because (y)/(x) =(1)/(X-1)]` |
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