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If lim(xto0) (1+ax+bx^(2))^(2//x)=e^(3),...

If `lim_(xto0) (1+ax+bx^(2))^(2//x)=e^(3)`, then find the values of a and b.

Text Solution

Verified by Experts

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.`
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