For the function \[f(x)=\left\{ \begin{align} & \frac{{{\sin }^{2}}ax}{{{x}^{2}}},\,\text{when}\,x\ne 0 \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,1,\text{when}\,x=0 \\ \end{align} \right.\] which one is a true statement

\[\underset{x\to 1}{\mathop{\lim }}\,(1-x+[x-1]+[1-x])\] is continuous at \[x=a\]

\[f(x)\]is continuous at \[x=0\]

\[f(x)\]is discontinuous at \[x=0\], when \[a\ne \pm 1\]

For the function \[f(x)=\left\{ \begin{align} & \frac{{{\sin }^{2}}

1.	For the function \[f(x)=\left\{ \begin{align} & \frac{{{\sin }^{2}}ax}{{{x}^{2}}},\,\text{when}\,x\ne 0 \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,1,\text{when}\,x=0 \\ \end{align} \right.\] which one is a true statement
A.	\[f(x)\]is continuous at \[x=0\]
B.	\[f(x)\]is discontinuous at \[x=0\], when \[a\ne \pm 1\]
C.	\[\underset{x\to 1}{\mathop{\lim }}\,(1-x+[x-1]+[1-x])\] is continuous at \[x=a\]
D.	None of these
Answer» C. \[\underset{x\to 1}{\mathop{\lim }}\,(1-x+[x-1]+[1-x])\] is continuous at \[x=a\]

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For the function \[f(x)=\left\{ \begin{align} & \frac{{{\sin }^{2}}ax}{{{x}^{2}}},\,\text{when}\,x\ne 0 \\ & \,\,\,\,\,\,\,\,\,\,\,\,\,\,1,\text{when}\,x=0 \\ \end{align} \right.\] which one is a true statement

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