Practicing Success
If the function $\left\{\begin{matrix}\frac{3}{x^2}\sin2x^2;&if\,\,x<0\\0;&if\,\,x=2\\\frac{x^2-3x+k}{1-3x^2};&if\,\,x≥0,x≠2\end{matrix}\right\}$ is continuous at x = 0, then the value of k is |
4 5 6 none of these |
6 |
$\underset{x→0-}{\lim}f(x)=\underset{x→0}{\lim}\frac{3}{x^2}\sin(2x^2)$ $=\underset{x→0}{\lim}\frac{6}{2x^2}\sin(2x^2)=6$ $\underset{x→0+}{\lim}f(x)=\underset{x→0}{\lim}\frac{x^2-3x+k}{1-3x^2}=k$ Since f (x) is continuous at x = 0 $∴\underset{x→0-}{\lim}f(x)=\underset{x→0+}{\lim}f(x)=f(0)$ $∴k = 6$ |