AP EAMCET · Maths · Limits
If \(\lim _{x \rightarrow 1} \frac{\sqrt[4]{x^{-3}}+a \sqrt[4]{x^5}}{x-1}=-2\), then the coefficient of \(x\) in the expansion of \(\left(\sqrt[4]{x^{-3}}+a \sqrt[4]{x^5}\right)^4\) is
- A \(6\)
- B \(-1\)
- C \(5\)
- D \(4\)
Answer & Solution
Correct Answer
(A) \(6\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} & \text {} \lim _{x \rightarrow 1} \frac{\sqrt[4]{x^{-3}}+a \sqrt[4]{x^5}}{x-1}=-2 \\ & \Rightarrow \lim _{x \rightarrow 1} \frac{\sqrt[4]{x^{-3}}\left(1+a x^2\right)}{x-1}=-2 \end{aligned}\) This is possible if and if \(a=1\)…
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