A) \[\underset{x\to a}{\mathop{\lim }}\,f(x)=a\]
B) \[f(x)\] is continuous at x = a
C) \[f(x)\] is discontinuous at x = a
D) None of these
Correct Answer: B
Solution :
[b] \[f(a)=0\] \[\underset{x\to a-}{\mathop{\lim }}\,f(x)=\underset{x\to a-}{\mathop{\lim }}\,\left( \frac{{{x}^{2}}}{a}-a \right)=\underset{h\to 0}{\mathop{\lim }}\,\left\{ \frac{{{\left( a-h \right)}^{2}}}{a}-a \right\}=0\] and \[\underset{x\to a+}{\mathop{\lim }}\,f(x)=\underset{h\to 0}{\mathop{\lim }}\,\left\{ a-\frac{{{\left( a+h \right)}^{2}}}{a} \right\}=0\] Hence it is continuous at \[x=a\].
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