Let $f\left( a \right) = g\left( a \right) = k$ and their nth derivatives ${f^n}\left( a \right),{g^n}\left( a \right)$ exist and are not equal for somen. Further if $\mathop {\lim }\limits_{x \to a} \frac{{f\left( a \right)g\left( x \right) - f\left( a \right) - g\left( a \right)f\left( x \right) + g\left( a \right)}}{{g\left( x \right) - f\left( x \right)}} = 4$, then the value of $k$ is equal to

JEE MATHEMATICS MCQ: LIMITS

1 Easy

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Analyzing +4 | -1

Let

f\left( a \right) = g\left( a \right) = k

and their nth derivatives

{f^n}\left( a \right),{g^n}\left( a \right)

exist and are not equal for somen. Further if

\lim\limits_{x \to a} \frac{{f\left( a \right)g\left( x \right) - f\left( a \right) - g\left( a \right)f\left( x \right) + g\left( a \right)}}{{g\left( x \right) - f\left( x \right)}} = 4

, then the value of

k

is equal to

View answer and explanation

Correct option: A

Option A (4) is correct because by applying L'Hôpital's rule, the limit simplifies to k, which is equal to 4.