AP EAMCET · Maths · Limits
\(\lim _{x \rightarrow 0}\left(\frac{\sin \left(\pi \cos ^2 x\right)}{x^2}\right)=\)
- A \(-\pi\)
- B \(\pi\)
- C \(\frac{\pi}{2}\)
- D 1
Answer & Solution
Correct Answer
(B) \(\pi\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \text { } \lim _{x \rightarrow 0} \frac{\sin \left(\pi \cos ^2 x\right)}{x^2}=\lim _{x \rightarrow 0} \frac{\sin \left(\pi-\pi \sin ^2 x\right)}{x^2} \\ & =\lim _{x \rightarrow 0} \frac{\sin \left(\pi \sin ^2 x\right)}{x^2}=\lim _{x \rightarrow 0} \frac{\sin…
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
- If \(12^{4+2 x^2}=(24 \sqrt{3})^{3 x^2-2}\), then \(x\) is equal toAP EAMCET 2016 Easy
- In a \(\triangle A B C, \operatorname{cosec} A(\sin B \cdot \cos C+\cos B \cdot \sin C)\) equals toAP EAMCET 2021 Medium
- If \(A=\left[\begin{array}{cc}\cos \theta & \sin \theta \\ -\sin \theta & \cos \theta\end{array}\right]\) and \(A^3=\left[\begin{array}{cc}\cos 3 \theta & m \\ n & \cos 3 \theta\end{array}\right]\), the values of \(m\) and \(n\) respectively areAP EAMCET 2020 Easy
- In \(\triangle A B C\), if \(\theta\) is any angle, then \(b \cos (C+\theta)+c \cos (B-\theta)=\)AP EAMCET 2017 Medium
- If \(\sin x \cosh y=\cos \theta\) and \(\cos x \sinh y=\sin \theta\), then \(\sin ^2 x+\cosh ^2 y=\)AP EAMCET 2023 Medium
- If 12 dice are thrown at a time, then the probability that a multiple of 3 does not appear on any dice isAP EAMCET 2024 Medium
More PYQs from AP EAMCET
- If \(z_1=10+6 i, z_2=4+6 i\) an \(z\) is any complex number such that the argument of \(\frac{\left(z-z_1\right)}{\left(z-z_2\right)}\) is \(\frac{\pi}{4}\), thenAP EAMCET 2024 Medium
- When the temperature of a gas is increased from to , the root mean square speed of the gas wouldAP EAMCET 2021 Easy
- The centripetal acceleration ' \(a\) ' of an electron in an orbit of hydrogen and the principal quantum number ' \(n\) ' of the orbit are related byAP EAMCET 2023 Easy
- \(\left|\begin{array}{lll}125 & 5 & 25 \\ 343 & 7 & 49 \\ 729 & 9 & 81\end{array}\right|=\)AP EAMCET 2018 Easy
- If \(A=\left[\begin{array}{cc}0 & -1 \\ 1 & 0\end{array}\right]\), then the incorrect option among the following isAP EAMCET 2018 Easy
- If \(\cos \alpha+4 \cos \beta+9 \cos \gamma=0\) and \(\sin \alpha+4 \sin \beta+9 \sin \gamma=0\), then \(81 \cos (2 \gamma-2 \alpha)-16 \cos (2 \beta-2 \alpha)=\)AP EAMCET 2024 Hard