1.

Let a `gt` 0 be real number. Then the limit `lim_(xto2) (a^(x)+a^(3-x)-(a^(2)+a))/(a^(3-x)-a^(x//2))` is-A. 2 log aB. `-(4)/(3)` aC. `(a^(2)+a)/(2)`D. `(2)/(3)(1-a)`

Answer» Correct Answer - D
`underset(xto2)lim(a^(x)+a^(3-x)-(a^(2)+a))/(a^(3-x)-a^(x//2))((0)/(0))`
Apply L hospital rule
`underset(xto2)lim(a^(x)lna-a^(3-x)lna)/(-a^(3-x)lna-(1)/(2)a^(x//2lna))`
`(a^(2)lna-alna)/(-alna-(a)/(2)lna)=(a^(2)-a)/(-(3a)/(2))=(2)/(3)(1-a)`


Discussion

No Comment Found

Related InterviewSolutions