A) 8
B) 16
C) 4
D) Does not exist
Correct Answer: C
Solution :
[c] \[\underset{x\to 0}{\mathop{\lim }}\,\frac{f({{x}^{2}}+x+1)-f(1)}{f({{x}^{4}}-{{x}^{2}}+2x+4)-f(4)}\] \[\left( \frac{0}{0}from \right)\] \[=\underset{x\to 0}{\mathop{\lim }}\,\frac{(2x+1)f'({{x}^{2}}+x+1)}{(4{{x}^{3}}-2x+2)f'({{x}^{4}}-{{x}^{2}}+2x+4)}=\frac{f'(1)}{2f'(4)}=4\] (Applying L' Hospital's Rule)You need to login to perform this action.
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