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Let underset(xto1)lim(x^(a)-ax+a-1)/((x-...

Let `underset(xto1)lim(x^(a)-ax+a-1)/((x-1)^(2))=f(a)`. Then the value of `f(4)` is_________.

A

`-4`

B

1

C

`-7`

D

5

Text Solution

Verified by Experts

The correct Answer is:
C
`underset(x rarr1)("lim") (x^(2) - ax + b)/(x -1)`
`1 -a.1 + b = 0` ....(1)
`underset(x rarr 1)(lim) (2x -a)/(1) = 5`
`2 - a = 5 rArr a = -3` ....(2)
From (1) and (2) `b = -4`
`:. a + b = -7`
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