AP EAMCET · Maths · Limits
If \(\lim _{x \rightarrow \infty} \frac{(\sqrt{2 x+1}+\sqrt{2 x-1})^8+(\sqrt{2 x+1}-\sqrt{2 x-1})^8\left(P x^4-16\right)}{\left(x+\sqrt{x^2-2}\right)^8+\left(x-\sqrt{x^2-2}\right)^8}\) \(=1\), then \(P=\)
- A 16
- B 64
- C \(\frac{1}{64}\)
- D \(\frac{1}{16}\)
Answer & Solution
Correct Answer
(D) \(\frac{1}{16}\)
Step-by-step Solution
Detailed explanation
\(\lim _{x \rightarrow \infty} \frac{\left[(\sqrt{2 x+1}+\sqrt{2 x-1})^8+(\sqrt{2 x+1}-\sqrt{2 x-1})^8\right]\left(P x^4-16\right)}{\left(x+\sqrt{x^2-2}\right)^8+\left(x-\sqrt{x^2-2}\right)^8}\) Dividing numerator and denominator by \(x^8\)…
See the Complete Solution
Get step-by-step explanations for this and 2.5 Lakh+ more JEE, NEET & CET questions.
- Unlock all solutions
- Practice the full chapter
- Track accuracy across PYQs
4.8 rated on Google Play · 14,000+ reviews
More questions from Maths
- \(\mathrm{A}(4,3), \mathrm{B}(2,5)\) are two points. If P is a variable point on the same side as that of the origin with respect to the line AB and is at most at a distance of 5 units from the midpoint of \(A B\), then the locus of \(P\) isAP EAMCET 2025 Medium
- \(\frac{1}{1.5}+\frac{1}{5.9}+\frac{1}{9.13}+\ldots\) upto \(n\) terms \(=\)AP EAMCET 2024 Easy
- If \(\sum_{i=1}^9\left(x_i-5\right)=9\) and \(\sum_{i=1}^9\left(x_i-5\right)^2=45\), then the standard deviation of the nine observations \(\mathrm{x}_1, \mathrm{x}_2, \ldots, \mathrm{x}_9\) isAP EAMCET 2025 Medium
- \(A(3,2,-1), B(4,1,1), C(6,2,5)\) and \(D(3,3,3)\) are four points. \(G_1, G_2, G_3\) and \(G_4\) respectively are the centroids of the triangles \(\triangle B C D, \triangle C D A\), \(\triangle D A B\) and \(\triangle A B C\). The point of concurrence of the lines \(A G_1, B G_2, C G_3\) and \(D G_4\) isAP EAMCET 2018 Easy
- If the angle between the pair of lines \(x^2+2 \sqrt{2} x y+k y^2\) \(=0, \mathrm{k}>0\) is \(45^{\circ}\), then the area (in square units) of the triangle formed by the pair of bisectors of the angles between these lines and the line \(x+2 y+1=0\) isAP EAMCET 2023 Medium
- If the mean and variance of a binomial variable \(X\) are 2 and 1 respectively, then \(P(X \geq 1)\) is equal toAP EAMCET 2010 Easy
More PYQs from AP EAMCET
- The number of those tangents to the curve which pass through the point isAP EAMCET 2022 Easy
- If the letters of the word "CAPITAL" are permuted in all possible ways and the words are arranged in a dictionary order, then the rank of the word "CAPITAL" isAP EAMCET 2017 Medium
- \(\mathrm{C}_6 \mathrm{H}_5 \mathrm{NH}_2 \xrightarrow[\substack{\mathrm{HCl} \\ 0-5^{\circ} \mathrm{C}}]{\mathrm{NaNO}_2} \mathrm{X} \xrightarrow[\mathrm{HCl}]{\mathrm{CuCl}} \mathrm{Y} \xrightarrow[\text { dryether }]{\mathrm{CH}_3 \mathrm{Cl} \mid \mathrm{Na}} \mathrm{Z}\)
What is \(\mathrm{Z}\) in the sequence of reactions?AP EAMCET 2017 Hard - If \(E_c\) and \(E_m\) are peak values of carrier and modulating signals, respectively then for \(100 \%\) modulation,AP EAMCET 2019 Easy
- Match the following
AP EAMCET 2018 Easy - If \(\sec (\theta+\alpha), \sec \theta\) and \(\sec (\theta-\alpha)\) are arithmetic progression, then \(\sin ^2 \theta=\)AP EAMCET 2023 Easy