Advertisement Remove all ads

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

Advertisement Remove all ads
Advertisement Remove all ads
Advertisement Remove all ads

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

Advertisement Remove all ads

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
  Is there an error in this question or solution?

APPEARS IN

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

Video TutorialsVIEW ALL [1]

Advertisement Remove all ads
Share
Notifications

View all notifications


      Forgot password?
View in app×