A) 1
B) 0
C) \[\infty \]
D) Does not exist
Correct Answer: D
Solution :
\[Rf'(0)=\underset{h\to 0}{\mathop{\lim }}\,\frac{f(0+h)-f(0)}{h}=\underset{h\to 0}{\mathop{\lim }}\,\frac{1+\sinh -1}{h}=1\] \[f'(0)=\underset{h\to 0}{\mathop{\lim }}\,\frac{f(0-h)-f(0)}{-h}=\underset{h\to 0}{\mathop{\lim }}\,\frac{1-1}{-h}=0\] Hence, \[f'(0)\] does not exist.
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