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The function $f(x)=\large\frac{ln(1+ax)-ln(1-bx)}{x}$ is not defined at $x=0$. The value which should be assigned to $f$ at $x=0$ so that it is continuous at $x=0$ is

$(a)\;a-b\qquad(b)\;a+b\qquad(c)\;ln a-ln b\qquad(d)\;None\;of\;these$

Can you answer this question?
 
 

1 Answer

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For $f(x)$ to be continuous at x=0
$f(0)=\lim\limits_{x\to 0}f(x)$
$\qquad=\lim\limits_{x\to 0}\large\frac{ln(1+ax)-ln(1-bx)}{x}$
Using $\lim\limits_{x\to 0}\large\frac{ln(1+x)}{x}$$=1$
$\Rightarrow a+b$
Hence (b) is the correct answer.
answered Jan 3, 2014 by sreemathi.v
 

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