question_answer

Let \[f\left( x= \right)\left\{ \begin{matrix}    \frac{\begin{matrix}    \left( 3/{{x}^{2}} \right)\sin \,2{{x}^{2}}  \\    {{x}^{2}}+2x+c  \\ \end{matrix}}{1-3{{x}^{2}}}  \\    0  \\ \end{matrix} \right.\begin{matrix}    x<0  \\    x\,\,\underline{>}\,\,0,\,x\ne \frac{1}{\sqrt{3}}.  \\    x=\frac{1}{\sqrt{3}}  \\ \end{matrix}\] If f be continuous at\[x=0\], then find value of c.

Answer:

6.00