List of top Mathematics Questions on Limits asked in MET

The value of \(\lim_{n \to \infty} \left[\sqrt[3]{n^2 - n^3} + n\right]\) is
\(\lim_{n \to \infty} \left( \frac{1^2}{1 - n^3} + \frac{2^2}{1 - n^3} + \dots + \frac{n^2}{1 - n^3} \right)\) is equal to
The value of \(\lim_{x \to \pi/6} \frac{\sin x + \sin 2x - 1}{\sin 2x - \sin 3x + 1}\) is

Evaluate the integral:  

\[ \int \frac{\sec^2 x}{(\sec x + \tan x)^{9/2}} \, dx \]

\(\lim_{x \to -1} \left( \frac{x^4 + x^2 + x + 1}{x^2 - x + 1} \right)^{\frac{1 - \cos(x+1)}{(x+1)^2}}\) is equal to
The approximate value of \((1.0002)^{3000}\) is
If \(\tan A\) and \(\tan B\) are the roots of the equation \(x^2 - ax + b = 0\), then the value of \(\sin^2(A + B)\) is
The reflection of the point (2, 1, 3) in the plane $3x-2y-z=9$ is