A) \[\underset{x\to 0}{\mathop{\lim }}\,f(x)\] does not exist
B) \[f(x)\]is continuous at \[x=0\]
C) \[f(x)\] is not differentiable at \[x=0\]
D) \[f(x)=1\]
Correct Answer: B
Solution :
Given, \[f(x)=[{{\tan }^{2}}x]\] \[\therefore \]\[\underset{x\to 0}{\mathop{\lim }}\,f(x)=\underset{x\to 0}{\mathop{lim}}\,\,[{{\tan }^{2}}x]=0\] and \[f(0)=[ta{{n}^{2}}0]=0\] Thus, \[f(x)\]is continuous at \[x=0.\]
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