Question
Question: Let \(f(a) = g(a) = k\) and their \(n^{th}\) derivatives \(f^{n}(a),g^{n}(a)\) exist and are not equ...
Let f(a)=g(a)=k and their nth derivatives fn(a),gn(a) exist and are not equal for some n. If
limx→ag(x)−f(x)f(a)g(x)−f(a)−g(a)f(x)+g(a)=4, then the value of k is
A
4
B
2
C
1
D
0
Answer
4
Explanation
Solution
limx→ag(x)−f(x)kg(x)−kf(x)=4
By L-Hospital’ rule, limx→ak[g′(x)−f′(x)g′(x)−f′(x)]=4, ∴ k=4.