AP EAMCET · Maths · Limits
Find the value of \(\lim _{x \rightarrow 0} \frac{\sin \left(x^m\right)}{(\sin x)^n}\), given that \(n < m\)
- A 2
- B 1
- C 0
- D \(\infty\)
Answer & Solution
Correct Answer
(C) 0
Step-by-step Solution
Detailed explanation
\(\begin{aligned} \operatorname{Lim}_{x \rightarrow 0} & \frac{\sin \left(x^m\right)}{(\sin x)^n} ;(n n\} \\ & =0 \end{aligned}\) Hence, option (c) is correct.
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
- The equations \(x^2-a x+b=0\) and \(x^2+b x-a=0\) have a common root, thenAP EAMCET 2021 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
- The perimeter of a sector is constant. If its area is to be maximum, the sectorical angle should beAP EAMCET 2022 Easy
- If \(3 \sin ^4 x+2 \cos ^4 x=\frac{6}{5}\) and \(x\) is an acute angle, then \(\tan 2 \mathrm{x}=\)AP EAMCET 2023 Easy
- If the curves and intersect at right angles, thenAP EAMCET 2021 Medium
- \(\int_0^{\frac{\pi}{4}} \log (1+\tan x) d x=\)AP EAMCET 2024 Hard
More PYQs from AP EAMCET
- \(\lim _{x \rightarrow \infty} \frac{3 x+4 \cos ^2 x}{\sqrt{x^2-5 \sin ^2 x}}=\)AP EAMCET 2025 Medium
- The mole fractions of glucose and water in aqueous glucose solution are 0.0244 and 0.9756 respectively. What is the weight percentage ( \(\mathrm{w} / \mathrm{w}\) ) of glucose in this solution?AP EAMCET 2025 Medium
- The solution of the differential equation \(\left(1+y^2\right)+\left(x-e^{\tan ^{-1} y}\right) \frac{d y}{d x}=0\), isAP EAMCET 2016 Medium
- If \(a^2+b^2+c^2=1, a, b, c \in R\), then the set of extreme values of \(a b+b c+c a\) isAP EAMCET 2022 Medium
- The type of bond connecting two nucleotides isAP EAMCET 2018 Easy
- At any instant ' \(\mathrm{t}\) ' the vertical distance ' \(\mathrm{Y}\) ' and horizontal distance ' \(\mathrm{X}\) ' of a projectile are given by \(2 \mathrm{Y}=6 \mathrm{t}-\mathrm{gt}^2\) and \(X=4 \mathrm{t}\). The initial velocity of projectile is ( \(\mathrm{X}\) and \(\mathrm{Y}\) are in metre and \(\mathrm{t}\) is in second)AP EAMCET 2023 Easy