AP EAMCET · Maths · Limits
\(\lim _{x \rightarrow 0} \frac{8}{\sin ^8 x}\) \(\left\{1-\cos \left(\frac{x^2}{2}\right)-\cos \left(\frac{x^2}{4}\right)+\cos \left(\frac{x^2}{2}\right) \cos \left(\frac{x^2}{4}\right)\right\}=\)
- A \(\frac{1}{16}\)
- B \(\frac{1}{32}\)
- C \(\frac{1}{64}\)
- D \(\frac{1}{8}\)
Answer & Solution
Correct Answer
(B) \(\frac{1}{32}\)
Step-by-step Solution
Detailed explanation
\(\begin{aligned} \lim _{x \rightarrow 0} \frac{8}{\sin ^8 x}\left\{1-\cos \left(\frac{x^2}{2}\right)-\right. & \cos \left(\frac{x^2}{4}\right) \\ & \left.+\cos \left(\frac{x^2}{2}\right) \cdot \cos \left(\frac{x^2}{4}\right)\right\} \end{aligned}\)…
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
- An urn \(A\) contains 3 white and 5 black balls. Another urn \(B\) contains 6 white and 8 black balls. A ball is picked from A at random and then transferred to \(B\). Then, a ball is picked at random from \(B\). The probability that it is a white ball isAP EAMCET 2010 Medium
- Bag \(A\) contains 6 Green and 8 Red balls and bag \(B\) contains 9 Green and 5 Red balls. A card is drawn at random from a well shuffled pack of 52 playing cards. If it is a spade, two balls are drawn at random from bag \(A\), otherwise two balls are drawn at random from bag \(B\). If the two balls drawn are found to be of the same colour, then the probability that they are drawn from bag \(A\) isAP EAMCET 2019 Medium
- Let \(\omega=\operatorname{cis}\left(\frac{2 \pi}{3}\right)=\cos \left(\frac{2 \pi}{3}\right)+i \sin \left(\frac{2 \pi}{3}\right)\) and \(f(x)=x^7-2 x^4-4 x^3+8\). Which of the following option is correct?AP EAMCET 2021 Medium
- Let and be the sides of two squares such that . The rate of change of area of the second square with respect to the area of the first square isAP EAMCET 2021 Easy
- In a \(\triangle A B C\), if \(r_1>r_2>r_3\), then which of the following is true?AP EAMCET 2022 Medium
- If are position vectors of respectively and if are mid points of sides and , then is equal toAP EAMCET 2021 Easy
More PYQs from AP EAMCET
- If is a normal to the parabola then the condition isAP EAMCET 2022 Easy
- If the maximum and minimum voltages of an A.M wave are \(\mathrm{V}_{\max }\) and \(\mathrm{V}_{\text {min }}\) respectively, Then the modulation factor ' \(m\) ' isAP EAMCET 2024 Easy
- One mole of \(A(g)\) is heated to \(200^{\circ} \mathrm{C}\) in a one litre closed flask, till the following equilibrium is reached.
\(A(g) \quad B(g)\)
The rate of forward reaction at equilibrium is \(0.02 \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~min}^{-1}\). What is the rate (in \(\mathrm{mol} \mathrm{L}^{-1} \mathrm{~min}^{-1}\) ) of the backward reaction at equilibrium?AP EAMCET 2002 Easy - The power of the point \(B(-1,1)\) with respect to the circle \(S \equiv x^2+y^2-2 x-4 y+3=0\) is \(p\). If the length of the tangent drawn from \(B\) to the circles \(S=0\) is \(t\), then the point \((2,3)\) with respect to the circle \(S^{\prime}=0\) having centre at \(\left(p, t^2\right)\) and passing through the origin.AP EAMCET 2019 Hard
- Consider the following reaction
\(\mathrm{N}_2(g)+3 \mathrm{H}_2(g) \longrightarrow 2 \mathrm{NH}_3(g)\)
The rate of this reaction in terms of \(\mathrm{N}_2\) at \(T \mathrm{~K}\) is \(\frac{-d\left[\mathrm{~N}_2\right]}{d t}=0.02 \mathrm{~mol} \mathrm{~L}^{-1} \mathrm{~s}^{-1}\). What is the value of \(-d\left[\mathrm{H}_2\right] / d t\) (in units of \(\mathrm{mol} \mathrm{L}^{-1} \mathrm{~s}^{-1}\) ) at the same temperature.AP EAMCET 2019 Medium - Two infinite long wires each carrying a current \(10 \mathrm{~A}\) are bend to form a right angle as shown in the figure. Then the magnetic induction at ' \(\mathrm{O}\) ' is \(\left[\mu_0=4 \pi \times 10^{-7} \mathrm{Hm}^{-1}\right]\)
AP EAMCET 2017 Easy