Let `lim_(xto1) (x^(a)-ax+a-1)/((x-1)^(2))=f(a)`. Then the value of `f(4)` is_________.
Let `lim_(xto1) (x^(a)-ax+a-1)/((x-1)^(2))=f(a)`. Then the value of `f(4)` is_________.
A. `+-(pi)/(4)`
B. `+-(pi)/(3)`
C. `+-(pi)/(6)`
D. `+-(pi)/(2)`
4 views
1 Answers
Correct Answer - `(6)`
Put `x=1+h`. Then,
`f(a)=underset(hto0)lim((1+h)^(a)-a(1+h)+a-1)/(h^(2))`
`=underset(hto0)lim((1+ah+(a(a-1))/(2!)h^(2)+...)-a-ah+a-1)/(h^(2))`
`:.f(a)=(a(a-1))/(2)`
`:.f(4)=6`
4 views
Answered