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Let `lim_(x to) (1+(P(x))/(x^(5)))^((1)/(x^(3)-tan^(3)x))` exists and is equal to `e^(9//7)`, where P(x) is a polynormial function. The degree of polynomial isA. 8B. 9C. 10D. 11 |
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Answer» Correct Answer - A `underset(xto0)lim(1+(P(x))/(x^(5)))^((1)/(x^(3)-tan^(3)x))=e^(9//7)` `:.P(x)` must be of degree greater than or equal to 6 `i.e.P(x)=ax^(6)+bx^(7)+. . . . . . . . . . . .. ` `underset(xto0)lime^(underset(xto0)lim(1)/((x^(3)-tan^(3)x))(1+(P(x))/(x^(2))-1))=e^(9//7)` `underset(xto0)lim((x^(3))/(x-tanx))((x^(2))/(x^(2)+tan^(2)x+xtanx))(P(x))/(x^(5).x^(5))=(9)/(7)` `(-3)(2)underset(xto0)lim(P(x))/(x^(10))=(9)/(7)` `underset(xto0)lim(P(x))/(x^(10))=(-3)/(14)` Hence degree of P(x) is 10 |
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