Let f(a) = g(a) = k and their n^(t)h 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

Limit, Continuity and Differentiability: JEE Main 2003 Mathematics question

JEE Main 2003 · Annual, Paper 1 · Q4170

JEE Main 2003Annual, Paper 1MathematicsMediumLimit, Continuity and Differentiability420× since 2002

Let

f(a) = g(a) = k

and their n^th derivatives

{f^n}(a)

{g^n}(a)

exist and are not equal for some n. Further if

\mathop {\lim }\limits_{x \to a} {{f(a)g(x) - f(a) - g(a)f(x) + f(a)} \over {g(x) - f(x)}} = 4

then the value of k is

JEE Main 2003 · Annual, Paper 1 · Q4170

JEE Main 2003Annual, Paper 1MathematicsMediumLimit, Continuity and Differentiability420× since 2002

Let

f(a) = g(a) = k

and their n^th derivatives

{f^n}(a)

{g^n}(a)

exist and are not equal for some n. Further if

\mathop {\lim }\limits_{x \to a} {{f(a)g(x) - f(a) - g(a)f(x) + f(a)} \over {g(x) - f(x)}} = 4

then the value of k is