JEE Mains · Maths · STD 11 - 12. limits
If \(\lim _{x \rightarrow 1} \frac{(5 x+1)^{1 / 3}-(x+5)^{1 / 3}}{(2 x+3)^{1 / 2}-(x+4)^{1 / 2}}=\frac{m \sqrt{5}}{n(2 n)^{2 / 3}}\), where \(\operatorname{gcd}(m, n)=1\), then \(8 m+12 n\) is equal to ...........
- A \(100\)
- B \(200\)
- C \(300\)
- D \(400\)
Answer & Solution
Correct Answer
(A) \(100\)
Step-by-step Solution
Detailed explanation
\( \lim _{x \rightarrow 1} \frac{\frac{1}{3}(5 x+1)^{-2 / 3} 5-\frac{1}{3}(x+5)^{-2 / 3}}{\frac{1}{2}(2 x+3)^{-1 / 2} \cdot 2-\frac{1}{2}(x+4)^{-1 / 2}} \) \(=\frac{8}{3} \frac{\sqrt{5}}{6^{2 / 3}} \quad \begin{gathered}\mathrm{m}=8 \\ \mathrm{n}=3\end{gathered}\)…
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