`lim_(x to0) ((1+a^(3))+8e^(1//x))/(1+(1-b^(3))e^(1//x))=2 " then "-`

Options

A. `a= 1,b=2`
B. `a= 1, b=(-3)^(1//3)`
C. `a=2, b=3 (1)/(3)`
D. None of these

Answer

B

Explanation

`underset(h to 0)("lim") ((1+a^(3)) +8e^(1//h))/(1+(1-b^(3))e^(1//h))=2`
`underset(h to 0)("lim") ((1+a^(3))/(e^(1//h))+8)/((1)/(e^(1//h))+1-b^(3)) =2 rArr (8)/(1-b^(3)) =2`
`rArr b^(3) =- e b=- 3^(1//3)`
`L.H.L`
`underset(h to 0)("lim") ((1+a^(3)) + 8e^(-1//h))/(1+(1-b^(3))e^(-1//h))=2 rArr 1+ a^(3) =2`
`rArr a=1`