If `lim_(xrarr0)(1+ax+bx^2)^(2//x)=e^3`, then the value of a and b, is :

Explanation

We have
`underset(xto0)lim(1+ax+bx^(2))^(2//x)=e^(3)" "(1^(oo)"from")`
`implies" "(underset(xto0)lim(1+ax+bx^(2))^((1)/(ax+bx^(2))))^((2(ax+bx^(2)))/(x))=e^(3)`
`implies" "e^(2a)=e^(3)`
`implies" "2a=3`
`implies" "a=3//2" and "binR.`