If $f\left( x \right)$ has a derivative at $x = a,$ then $\mathop {\lim }\limits_{x \to a} \frac{{xf\left( a \right) - af\left( x \right)}}{{x - a}}$ is equal to

$af\left( a \right) - f'\left( a \right)$

$f\left( a \right) + f'\left( a \right)$

$af\left( a \right) + f'\left( a \right)$

JEE MATHEMATICS MCQ: DIFFERENTIATION

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Analyzing +4 | -1

f\left( x \right)

has a derivative at

x = a,

then

\lim\limits_{x \to a} \frac{{xf\left( a \right) - af\left( x \right)}}{{x - a}}

is equal to

View answer and explanation

Correct option: A

f\left( a \right) - af'\left( a \right)

Option A (

f\left( a \right) - af'\left( a \right)

) is correct because by adding and subtracting

af(a)

in the numerator and applying L'Hopital's rule, the limit simplifies to this expression.