A) 0
B) -1
C) 1
D) e
Correct Answer: C
Solution :
Given, \[f(x)=\left\{ \begin{matrix} \frac{\log x}{x-1}, & if\,\,x\ne 1 \\ k\,\,\,\,\,\,\,\,\,\,, & if\,\,x=1 \\ \end{matrix} \right.\,\,at\,\,x=1\] Since, the function is continuous at \[x=1.\] Then, \[f\,\,\,(1)=\underset{x\to 1}{\mathop{lim}}\,\,f(x)\] \[k=\underset{x\to 1}{\mathop{\lim }}\,\,\,\frac{\log x}{x-1}\] \[\left( \frac{0}{0}\,\,from \right)\] Apply L?hospital rule, \[k=\underset{x\to 1}{\mathop{\lim }}\,\frac{1/x}{1}=\frac{1/1}{1}\] \[\Rightarrow \] \[k=1\]You need to login to perform this action.
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