A) Statement-1 is true, Statement-2 is true; Statement-2 is a correct explanation for Statement-1.
B) Statement-1 is true, Statement-2 is true; Statement-2 is NOT a correct explanation for Statement-1
C) Statement-1 is true, Statement-2 is false
D) Statement-1 is false, Statement-2 is true
Correct Answer: B
Solution :
\[f(x)=\left\{ \begin{matrix} x\sin (1/x), & x\ne 0 \\ 0, & x=0 \\ \end{matrix} \right.\] at\[x=0\] \[LHL=\underset{h\to {{0}^{+}}}{\mathop{\lim }}\,\left\{ -h\sin \left( -\frac{1}{h} \right) \right\}\] \[=0\times a\] finite quantity between - 1 and 1 \[RHL=\underset{h\to {{0}^{+}}}{\mathop{\lim }}\,h\,\sin \frac{1}{h}\] \[=0\] \[f(0)=0\] \[\therefore \]\[f(x)\]is continuous on R. \[{{f}_{2}}(x)\] is not continuous at x = 0You need to login to perform this action.
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