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The function $ \Large\frac{log(1+ax)-log(1-bx)}{x}$ is not defined at x = 0. Find the value of f(x) so that f(x) is continuous at x = 0.

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  • For $f(x)$ to be continuous at $ '0' LHL = RHL = f(0)$
  • $ \lim\limits_{x \to 0} \; \large\frac{log(1+x)}{x}=1$
LHL = RHL
$= \lim\limits_{x \to 0}\: \large\frac{log(1+ax)-log(1-bx)}{x}$
 
 
$= \lim\limits_{x \to 0}\: \large\frac{log(1+ax)}{ax}$x $ a-\lim\limits_{x \to 0}\: \large\frac{log(1-bx)}{x(-b)}$ x $ (-b)$
$ = a+b$
$ f(o) = a+b\: and $
$f(x)= \left\{ \begin{array}{1 1} \Large\frac{log(1+ax)-log(1-bx)}{x} & \quad ,\;x\neq0 \\ a+b & \quad ,\;x=0 \end{array} \right.$
 

 

answered Mar 11, 2013 by thanvigandhi_1
edited Mar 26, 2013 by thanvigandhi_1
 

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