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The value of the limit `lim_(x to 0) ((x)/(sinx))^(6//x^(2))` isA. eB. `e^(-1)`C. `e^(-1//6)`D. `e^(6)` |
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Answer» Correct Answer - A `underset(xto0)lim((x)/sinx)^(6//x^(2))" "(1)^(oo)` `underset(e)underset(" "xto0)(" "lim)(6)/(x^(2))((x)/(sinx)-1)` `underset(e)underset(" "xto0)(" "lim)(6)/(x^(2))((x-sinx)/(sinx))` `underset(e)underset(" "xto0)(" "lim)(6)/(x^(2)){(x-(x-x^(3)/(3!)+x^(5)/(5!) . . . . . .))/{x-(x-x^(3)/(3!)+x^(5)/(5!) . . . . . .)}}` `underset(e)underset(" "xto0)(" "lim)(6)/(x^(2)){{(x^(3))/(3!)-x^(5)/(5!) . . . . . .}}/((x-x^(3)/(3!)+x^(5)/(5!) . . . . . .))` `underset(e)underset(" "xto0)(" "lim)(6x^(3))/(x^(2)){{(1)/(3!)-x^(5)/(5!) . . . . . .}}/{{1-x^(2)/(3!) . . . . . .}}=e^(1)` |
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