AP EAMCET · Maths · Limits
If \(f(x)=\left|\begin{array}{ccc}1 & 6+x & 36+x^2 \\ 0 & x-3 & 3 x^2-27 \\ 0 & 2 x-4 & 8 x^2-32\end{array}\right|\), then \(\lim _{x \rightarrow 1} \frac{f(x)}{f(-x)}=\)
- A \(2\)
- B \(-1\)
- C \(0\)
- D \(1\)
Answer & Solution
Correct Answer
(C) \(0\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text {} \because f(\mathrm{x})=\left|\begin{array}{ccc}1 & 6+x & 36+x^2 \\ 0 & x-3 & 3 x^2-27 \\ 0 & 2 x-4 & 8 x^2-32\end{array}\right| \\ & =1\left[(x-3)\left(8 x^2-32\right)-(2 x-4)\left(3 x^2-27\right)\right]+0 \\ & =8 x^3-32 x-24 x^2+96-\left(6 x^3-54 x-12…
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