Question:
The value of \( \lim_{x \to 0} \frac{\sin(5x)}{\sin(3x)} \) is:
The value of \( \lim_{x \to 0} \frac{\sin(5x)}{\sin(3x)} \) is:
Show Hint
Use standard limit properties for trigonometric functions when \( x \to 0 \).
Updated On: Mar 7, 2025
- \( \frac{3}{5} \)
- \( \frac{5}{3} \)
- 1
- 0
- 5
Hide Solution
Verified By Collegedunia
The Correct Option is B
Solution and Explanation
We know that:
\[
\lim_{x \to 0} \frac{\sin(kx)}{x} = k
\]
Using this, we have:
\[
\lim_{x \to 0} \frac{\sin(5x)}{\sin(3x)} = \frac{5x}{3x} = \frac{5}{3}
\]
Was this answer helpful?
0
0
Top Questions on Integration
- $ \int \frac{e^{10 \log x} - e^{8 \log x}}{e^{6 \log x} - e^{5 \log x}} \, dx$ is equal to :
- Evaluate the integral: \[ \int \frac{\sqrt{\tan x}}{\sin x \cos x} \, dx \]
- MHT CET - 2025
- Mathematics
- Integration
- For a function $f(x)$, which of the following holds true?
- Evaluate \( \int_0^{\frac{\pi}{2}} \frac{x}{\cos x + \sin x} \, dx \)
- Find \( \int \frac{3x + 1}{(x - 2)^2 (x + 2)} \, dx \)
View More Questions
Questions Asked in KEAM exam
- Benzene when treated with Br\(_2\) in the presence of FeBr\(_3\), gives 1,4-dibromobenzene and 1,2-dibromobenzene. Which type of reaction is this?
- KEAM - 2025
- Haloalkanes and Haloarenes
- 10 g of (90 percent pure) \( \text{CaCO}_3 \), treated with excess of HCl, gives what mass of \( \text{CO}_2 \)?
- KEAM - 2025
- Stoichiometry and Stoichiometric Calculations
- Evaluate the following limit: $ \lim_{x \to 0} \frac{1 + \cos(4x)}{\tan(x)} $
- KEAM - 2025
- Limits
- Given that \( \mathbf{a} \times (2\hat{i} + 3\hat{j} + 4\hat{k}) = (2\hat{i} + 3\hat{j} + 4\hat{k}) \times \mathbf{b} \), \( |\mathbf{a} + \mathbf{b}| = \sqrt{29} \), \( \mathbf{a} \cdot \mathbf{b} = ? \)
- KEAM - 2025
- Vector Algebra
- In an equilateral triangle with each side having resistance \( R \), what is the effective resistance between two sides?
- KEAM - 2025
- Combination of Resistors - Series and Parallel
View More Questions