KCET · Maths · Limits
The function \(f(x)=\frac{\log (1+a x)-\log (1-b x)}{x}\) is not defined at \(\mathrm{x}=0\). The value which should be assigned to \(\mathrm{f}\) at \(\mathrm{x}=0\) so that it is continuous at \(\mathrm{x}=0\) is
- A \(a-b\)
- B \(a+b\)
- C \(\log a+\log b\)
- D 0
Answer & Solution
Correct Answer
(B) \(a+b\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} \lim _{x \rightarrow 0} f(x) &=\lim _{x \rightarrow 0} \frac{\log (1+a x)-\log (1-b x)}{x} \\ &=\lim _{x \rightarrow 0} \frac{\frac{a}{1+a x}+\frac{b}{1-b x}}{1} \\ &=a+b \end{aligned}\)
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