Let f(a)=g(a)=k and their {\n}^{\text{th }} derivatives f^n(a), g^n(a) exist and are not equal for some {\n}. Further if \lim_{x \to a} \frac{f(a) g(x)-f(a)-g(a) f(x)+f(a)}{g(x)-f(x)}=4 then the value of k is [AIEEE 2003]

AIEEE 2003 Math Solved Paper

Section: Mathematics

Question : 62 of 66

Marks: +1, -0

Let f(a)=g(a)=k and their n‌th ‌ derivatives
fn(a),gn(a) exist and are not equal for some n. Further if

lim

x→a

‌

f(a)g(x)−f(a)−g(a)f(x)+f(a)

g(x)−f(x)

=4
then the value of k is

[AIEEE 2003]

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