1.

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 is

Answer»

8
9
10
11

Solution :`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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