JEE Mains · Maths · STD 11 - 12. limits
Let \( f:R\rightarrow(0,\infty) \) be a twice differentiable function such that \( f(3)=18, \) \( f^{\prime}(3)=0 \) and \( f^{\prime\prime}(3)=4 \). Then \( \lim_{x\rightarrow1}(\log_{e}(\frac{f(x+2)}{f(3)})^{\frac{18}{(x-1)^{2}}}) \) is equal to:
- A 1
- B 9
- C 2
- D 18
Answer & Solution
Correct Answer
(C) 2
Step-by-step Solution
Detailed explanation
Let \( T=\lim_{x\rightarrow1}(\frac{f(x+2)}{f(3)})^{\frac{18}{(x-1)^{2}}} \) ; \( 1^{\infty} \) form \( \Rightarrow T=e^{\lim_{x\rightarrow1}\frac{18}{(x-1)^{2}}(\frac{f(x+2)-f(3)}{f(3)})} \)…
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