A) 2
B) 4
C) 6
D) 8
Correct Answer: C
Solution :
[c] \[f'(5)=\underset{h\to 0}{\mathop{\lim }}\,\frac{f(5+h)-f(5)}{h}=\underset{h\to 0}{\mathop{\lim }}\,\frac{f(5+h)-f(5+0)}{h}\] \[=\underset{h\to 0}{\mathop{\lim }}\,\frac{f(5).f(h)-.f(0)}{h}[\because \,(x+y)=f(x).f(y)]\,\] \[=\underset{h\to 0}{\mathop{\lim }}\,\frac{f(5)[f(h)-f(0)]}{h}=f(5)\underset{h\to 0}{\mathop{\lim }}\,\frac{f(0+h)-f(0)}{h}\] \[=f\left( 5 \right).f'\left( 0 \right)=2\times 3=6\] Hence, option [c] is correct.You need to login to perform this action.
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