Question:
Let the slope of the line \( 45x + 5y + 3 = 0 \) be \( 27r_1 + \frac{9r_2}{2} \) for some \( r_1, r_2 \in \mathbb{R} \).Then\[\lim_{x \to 3} \left( \int_3^x \frac{8t^2}{\frac{3r_1 x}{2} - r_2 x^2 - r_1 x^3 - 3x} \, dt \right)\]is equal to _____.
Let the slope of the line \( 45x + 5y + 3 = 0 \) be \( 27r_1 + \frac{9r_2}{2} \) for some \( r_1, r_2 \in \mathbb{R} \).Then\[\lim_{x \to 3} \left( \int_3^x \frac{8t^2}{\frac{3r_1 x}{2} - r_2 x^2 - r_1 x^3 - 3x} \, dt \right)\]is equal to _____.
Updated On: Mar 20, 2025
Hide Solution
Verified By Collegedunia
Correct Answer: 12
Solution and Explanation
The Correct Answer is
Was this answer helpful?
0
0
Top Questions on Slope of a line
- A line passing through the point \( A(9, 0) \) makes an angle of \( 30^\circ \) with the positive direction of the x-axis. If this line is rotated about \( A \) through an angle of \( 15^\circ \) in the clockwise direction, then its equation in the new position is:
- JEE Main - 2024
- Mathematics
- Slope of a line
- Variance of 6, 7, 8, 9 is
- KEAM - 2024
- Mathematics
- Slope of a line
- If the slope of the line joining the points (4,2) and (3,-k) is -2, then the value of k is
- AP POLYCET - 2024
- Mathematics
- Slope of a line
- A thin particle moves from \((0,1)\) and gets reflected upon hitting the x-axis at \((√3,0)\). Then the slope of the reflected line is ?
- KEAM - 2023
- Mathematics
- Slope of a line
- The slope of the normal to the curve y = 2x2 + 3sinx at x = 0, is :
- CUET (UG) - 2023
- Mathematics
- Slope of a line
View More Questions
Questions Asked in JEE Main exam
- Let \( P_n = \alpha^n + \beta^n \), \( P_{10} = 123 \), \( P_9 = 76 \), \( P_8 = 47 \), and \( P_1 = 1 \). The quadratic equation whose roots are \( \frac{1}{\alpha} \) and \( \frac{1}{\beta} \) is:
- JEE Main - 2025
- Sequences and Series
- If \( \alpha + i\beta \) and \( \gamma + i\delta \) are the roots of the equation \( x^2 - (3-2i)x - (2i-2) = 0 \), \( i = \sqrt{-1} \), then \( \alpha\gamma + \beta\delta \) is equal to:
- JEE Main - 2025
- Matrices and Determinants
- The product B formed in the following reaction sequence is: \[ {C}_6{H}_5{CN} \xrightarrow{{HCl}} (A) \xrightarrow{{AgCN}} (B) \]
- JEE Main - 2025
- Organic Chemistry
- What are the units of viscosity, intensity of wave, and pressure gradient?
- JEE Main - 2025
- Units and measurement
- If the system of equations \[ (\lambda - 1)x + (\lambda - 4)y + \lambda z = 5 \] \[ \lambda x + (\lambda - 1)y + (\lambda - 4)z = 7 \] \[ (\lambda + 1)x + (\lambda + 2)y - (\lambda + 2)z = 9 \] has infinitely many solutions, then \( \lambda^2 + \lambda \) is equal to:
- JEE Main - 2025
- Matrices and Determinants
View More Questions