MCQ
Let $f(x) = \left[ {\begin{array}{*{20}{c}}
{a{{\cot }^{ - 1}}\left( {\frac{{b + x}}{4}} \right),\,\,\frac{{ - 2}}{3}\, < \,x\, < \,0} \\
{2\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,,\,x = 0} \\
{\frac{{\ln (1 - cx)}}{x},\,0\, < \,x\, < \,\frac{2}{3}}
\end{array}} \right.$ If the function $f(x)$ is differentiable at $x = 0,$ then find the value of $(b^2 -2a + c^6).$
{a{{\cot }^{ - 1}}\left( {\frac{{b + x}}{4}} \right),\,\,\frac{{ - 2}}{3}\, < \,x\, < \,0} \\
{2\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,,\,x = 0} \\
{\frac{{\ln (1 - cx)}}{x},\,0\, < \,x\, < \,\frac{2}{3}}
\end{array}} \right.$ If the function $f(x)$ is differentiable at $x = 0,$ then find the value of $(b^2 -2a + c^6).$
- A$18$
- B$38$
- C$0$
- ✓$48$