# Write the Value of Lim X → a X F ( a ) − a F ( X ) X − a - Mathematics

Write the value of $\lim_{x \to a} \frac{x f (a) - a f (x)}{x - a}$

#### Solution

$\lim_{x \to a} \frac{xf\left( a \right) - af\left( x \right)}{x - a}$
$= \lim_{x \to a} \frac{xf\left( a \right) - af\left( x \right) - xf\left( x \right) + xf\left( x \right)}{x - a}$
$= \lim_{x \to a} \frac{xf\left( a \right) - xf\left( x \right) + xf\left( x \right) - af\left( x \right)}{x - a}$
$= \lim_{x \to a} \frac{- x\left( f\left( x \right) - f\left( a \right) \right) + \left( x - a \right)f\left( x \right)}{x - a}$
$= \lim_{x \to a} - x \lim_{x \to a} \frac{f\left( x \right) - f\left( a \right)}{x - a} + \lim_{x \to a} \frac{\left( x - a \right)f\left( x \right)}{x - a}$
$= - a f'\left( a \right) + f(a)$


Concept: The Concept of Derivative - Algebra of Derivative of Functions
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#### APPEARS IN

RD Sharma Class 11 Mathematics Textbook
Chapter 30 Derivatives
Q 2 | Page 46