Question:
$\displaystyle\lim_{x\to0} \sqrt{\frac{x-\sin x}{x+\sin^{2}x}} $ is equal to
$\displaystyle\lim_{x\to0} \sqrt{\frac{x-\sin x}{x+\sin^{2}x}} $ is equal to
Updated On: Dec 19, 2025
- 1
- 0
- $\infty$
- None of these
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
$\displaystyle\lim_{x\to0} \sqrt{\frac{x-\sin x}{x+\sin^{2}x}} = \displaystyle\lim_{x\to0} \sqrt{\frac{1- \frac{\sin x}{x}}{1+ \frac{\sin^{2}x}{x}}} $
$=\displaystyle\lim_{x\to0} \sqrt{\frac{1- \frac{\sin x}{x}}{1+ \left(\frac{\sin x}{x}\right)\sin x}} = \sqrt{\frac{1-1}{1+1\times0}} = 0 $
$=\displaystyle\lim_{x\to0} \sqrt{\frac{1- \frac{\sin x}{x}}{1+ \left(\frac{\sin x}{x}\right)\sin x}} = \sqrt{\frac{1-1}{1+1\times0}} = 0 $
Was this answer helpful?
0
0
Top Questions on limits of trigonometric functions
- Find the value of the following expression: \[ \tan^2(\sec^{-1}4) + \cot(\csc^{-1}3) \]
- MHT CET - 2025
- Mathematics
- limits of trigonometric functions
- The value of \( \lim_{x \to 0} \left( \frac{\tan 11x}{\tan 5x} \right) \) is:
- GATE MN - 2025
- Engineering Mathematics
- limits of trigonometric functions
- Given a real-valued function \( f \) such that: \[ f(x) = \begin{cases} \frac{\tan^2\{x\}}{x^2 - \lfloor x \rfloor^2}, & \text{for } x > 0 \\ 1, & \text{for } x = 0 \\ \sqrt{\{x\} \cot\{x\}}, & \text{for } x < 0 \end{cases} \] Then:
- BITSAT - 2024
- Mathematics
- limits of trigonometric functions
- Evaluate the limit: \[ \lim_{\theta \to \frac{\pi}{2}} \frac{8\tan^4\theta + 4\tan^2\theta + 5}{(3 - 2\tan\theta)^4} \]
- TS EAMCET - 2024
- Mathematics
- limits of trigonometric functions
- If \( f(x) \) is defined as follows:
\[ f(x) = \begin{cases} \frac{x - \lfloor x \rfloor}{x - 2} & \text{if } x = 2 \\ \frac{|x - \lfloor x \rfloor|}{a^2 + (x - \lfloor x \rfloor)^2} & \text{if } 1 < x < 2 \\ 2a - b & \text{if } x = 1 \end{cases} \]
Then the limit \( \displaystyle \lim_{x \to 0} \frac{\sin(ax) + x \tan(bx)}{x^2} \) is:- AP EAPCET - 2023
- Mathematics
- limits of trigonometric functions
View More Questions
Questions Asked in BITSAT exam
- What is the dot product of the vectors \( \mathbf{a} = (2, 3, 1) \) and \( \mathbf{b} = (1, -1, 4) \)?
- BITSAT - 2025
- Vector Algebra
- Find the determinant of the matrix \( A = \begin{bmatrix} 2 & 3 \\ 4 & 5 \end{bmatrix} \).
- BITSAT - 2025
- Matrices
- A convex lens has focal length 20 cm. An object is placed at a distance of 40 cm from the lens. What is the position of the image formed?
- BITSAT - 2025
- Ray optics and optical instruments
- What is the value of \( \sin 30^\circ \)?
- BITSAT - 2025
- Trigonometry
- The area enclosed between the curve \(y = \log_e(x + e)\) and the coordinate axes is:
- BITSAT - 2025
- Fundamental Theorem of Calculus
View More Questions