AP EAMCET · Maths · Limits
\(\lim _{x \rightarrow 0} \frac{\tan ^3 x-\sin ^3 x}{x^5}\) is equal to
- A \(\frac{5}{2}\)
- B \(\frac{3}{2}\)
- C \(\frac{3}{5}\)
- D \(\frac{2}{5}\)
Answer & Solution
Correct Answer
(B) \(\frac{3}{2}\)
Step-by-step Solution
Detailed explanation
\begin{aligned} & \lim _{x \rightarrow 0} \frac{\tan ^3 x-\sin ^3 x}{x^5} \\ & =\lim _{x \rightarrow 0} \frac{\left[\begin{array}{c}\left(x+\frac{x^3}{3}+\frac{2}{15} x^5+\ldots\right)^3 \\ -\left(x-\frac{x^3}{3 !}+\frac{x^5}{5 !}+\ldots\right)^3\end{array}\right]}{x^5} \\ &…
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 \(\int e^x(1+x) \cdot \sec ^2\left(x e^x\right) d x\) \(=f(x)+\) constant, then \(f(x)\) is equal toAP EAMCET 2008 Medium
- The equation of the normal drawn at the point \((\sqrt{2}+1,-1)\) to the ellipse \(x^2+2 y^2-2 x+8 y+5=0\) isAP EAMCET 2025 Medium
- If the lines \(x^2+2 x y-35 y^2-4 x+44 y-12=0\) and \(5 x+k y-8=0\) are concurrent, then \(k\) equalsAP EAMCET 2021 Medium
- Let \(f(x)=x^2+2 x+2, g(x)=-x^2+2 x-1\) and \(a, b\) be the extreme values of \(f(x), g(x)\) respectively. If \(c\) is the extreme value of \(\frac{f}{g}(x)\) (for \(x \neq 1\) ), then \(a+2 b+5 c+4=\)AP EAMCET 2019 Medium
- A circle touches the line \(2 x+y-10=0\) at \((3,4)\) and passes through the point \((1,-2)\). Then a point that lies on the circle isAP EAMCET 2025 Medium
- Order and degree of the differential equation \(\frac{d^3 y}{d x^3}\left[1+\left(\frac{d y}{d x}\right)^2\right]^{5 / 2}\) respectively areAP EAMCET 2024 Easy
More PYQs from AP EAMCET
- If \(\mathrm{C}_{\mathrm{j}}\) stands for \({ }^{\mathrm{n}} \mathrm{C}_{\mathrm{j}}\), then
\(\frac{\mathrm{C}_0}{2}+\frac{\mathrm{C}_1}{2.2^2}+\frac{\mathrm{C}_2}{3.2^3}+\ldots+\frac{\mathrm{C}_{\mathrm{n}}}{(\mathrm{n}+1) 2^{\mathrm{n}+1}}=\)AP EAMCET 2023 Medium - \(\int \frac{\sin (2 x)}{\sin ^2(x)+2 \cos ^2(x)} d x=\)AP EAMCET 2020 Easy
- The geometries of \(\mathrm{XeF}_4\) and \(\mathrm{XeOF}_4\) respectively areAP EAMCET 2021 Easy
- The mass numbers of two elements \(X\) and \(Z\) are 52 and 75 respectively. \(X\) contains \(16.6 \%\) more neutrons compared to protons. \(Z\) contains \(27.3 \%\) more neutrons compared to protons. \(X\) and \(Z\) are respectivelyAP EAMCET 2018 Medium
- A hydrometer executes simple harmonic motion when it is pushed down vertically in a liquid of density . If the mass of hydrometer is and the radius of the hydrometer tube is , then the time period of oscillation isAP EAMCET 2022 Medium
- A Carnot engine operating between temperatures \(600 \mathrm{~K}\) and \(300 \mathrm{~K}\), absorbs \(800 \mathrm{~J}\) of heat from the source. The mechanical work done per cycle isAP EAMCET 2022 Easy