List of top Mathematics Questions on Limits asked in UPSEE

The $\displaystyle \lim_{x \to \frac{\pi}{2}} \left\{ 2x \tan x - \frac{\pi}{\cos x }\right\} $ is

Let $f(x) = \begin{cases} a (x) \sin \frac{\pi \ x }{2} & \text{for } x \neq 0 \\ -(n+1)/2 & \text{for} x = 0 \end{cases} $ where $\alpha (x) $ is such that $\displaystyle\lim_{x \to 0} |\alpha (x) | = \infty $ Then the function $f(x)$ is continuous at $x = 0$ if $\alpha (x) $ is chosen as

The $\displaystyle\lim_{y \to a} \left\{ \left(\sin \frac{y-a}{2}\right) . \left(\tan \frac{\pi y}{2a}\right)\right\} $ is

Let $l_{n } = \frac{2^{n } + \left(-2\right)^{n} }{2^{n}} $ and $L_{n} = \frac{2^{n} + \left(- 2\right)^{n}}{3^{n}}$ then as $ n \to\infty$

If function $f(x) = \begin{cases} x\, \sin\left(\frac{1}{x} \right) ; & \text{x $\ne$ 0} \\[2ex] a \,;& \text{x = 0} \end{cases}$ is continuous at $x = 0$, then value of $a$ is

Value of the following expression is $\displaystyle \lim_{n \to \infty}$$\frac{1}{n^{3}}\left(1^{2}+2^{2}+3^{2}+ ..... +n^{2}\right)$