A) \[\frac{\sum\limits_{i=1}^{n}{{{y}_{i}}}}{n}\]
B) \[\frac{\sum\limits_{i=1}^{n}{{{y}_{i}}}}{\sum\limits_{i=1}^{n}{i}}\]
C) \[\frac{\sum\limits_{i=1}^{n}{{{y}_{i}}}{{f}_{i}}}{n}\]
D) \[\frac{\sum\limits_{i=1}^{n}{{{y}_{i}}}{{f}_{i}}}{\sum\limits_{i=1}^{n}{{{f}_{i}}}}\]
Correct Answer: D
Solution :
\[Lf'(0)=\underset{h\to {{0}^{-}}}{\mathop{Lt}}\,\frac{f(0+h)-f(0)}{h}=\underset{h\to {{0}^{-}}}{\mathop{Lt}}\,\frac{-{{h}^{2}}-0}{h}=0\] &\[Rf'(0)=\underset{h\to {{0}^{+}}}{\mathop{Lt}}\,\frac{f(0+h)-f(0)}{h}=\underset{h\to {{0}^{+}}}{\mathop{Lt}}\,\frac{+{{h}^{2}}}{h}=0\] Hence, \[f(x)\] is differentiable at\[x=0\]
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