JEE Mains · Maths · STD 11 - 12. limits
\(\lim _{x \rightarrow \infty} \frac{\left(2 x^2-3 x+5\right)(3 x-1)^{\frac{x}{2}}}{\left(3 x^2+5 x+4\right) \sqrt{(3 x+2)^x}}\) is equal to :
- A \(\frac{2}{\sqrt{3 \mathrm{e}}}\)
- B \(\frac{2 \mathrm{e}}{\sqrt{3}}\)
- C \(\frac{2}{3 \sqrt{\mathrm{e}}}\)
- D \(\frac{2 \mathrm{e}}{3}\)
Answer & Solution
Correct Answer
(C) \(\frac{2}{3 \sqrt{\mathrm{e}}}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \lim _{x \rightarrow \infty} \frac{\left(2 x^2-3 x+5\right)(3 x-1)^{x / 2}}{\left(3 x^2+5 x+4\right) \sqrt{(3 x+2)^x}} \\ & =\lim _{x \rightarrow \infty} \frac{x^2\left(2-\frac{3}{x}+\frac{5}{x^2}\right)(3…
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