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The function \mathrm{ f(x)=\left\{\frac{\ln (1+a x)-\ln (1-b x)}{x}\right\} }is not defined at x=0. The value that should be assigned to f at x=0 in order to render it continuous at x=0 is

Option: 1

(a-b)


Option: 2

(a+b)


Option: 3

ln (a b)


Option: 4

ln (a / b)


Answers (1)

best_answer

By L. Hospital's rule,

\mathrm{\begin{aligned} \lim _{x \rightarrow 0} f(x) & =\lim _{x \rightarrow 0}\left\{\frac{\frac{a}{(1+a x)}+\frac{b}{(1-b x)}}{1}\right\} \\ & =(a+b) . \end{aligned}}

For continuity at x=0, \mathrm{\lim _{x \rightarrow 0} f(x)=f(0) \Rightarrow \quad f(0)=(a+b). }

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shivangi.bhatnagar

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