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Let f(a)=g(a)=k and their n^th order der...

Let `f(a)=g(a)=k` and their `n^th` order derivatives `f^n(a),g^n(a)` exist and are not equal for some `n in N`. Further, if
`lim_(xtoa)(f(a)g(x)-f(a)-g(a)f(x)+g(a))/(g(x)-f(x))=4`, then the value of k, is

A

0

B

4

C

2

D

1

Text Solution

Verified by Experts

The correct Answer is:
B
As given expression of form `(rarr0)/(rarr0)` we can use L Hospitals Rule
`implies lim_(x rarra)(f(a)g(x)-g(a)f(x))/(g(x)-f(x))implies ((g(x)-f(x)))/((g(x)-f(x)))=4` Given g(a) `ne` f(a)
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