List of top Mathematics Questions on Limits asked in KCET

The value of \[ \lim_{x \to 1} \frac{x^4 - \sqrt{x}}{\sqrt{x} - 1} \] is:
A function \( f(x) \) is given by:
\[ f(x) = \begin{cases} \frac{1}{e^x - 1}, & \text{if } x \neq 0 \\ \frac{1}{e^x + 1}, & \text{if } x = 0 \end{cases} \] Then, which of the following is true?
$\lim_{x \to \frac{\pi}{4}} \frac{\sqrt{2}\cos x - 1}{\cot x - 1}$ is equal to:
$\lim_{n \to \infty} \left(\frac{n}{n^2 + 1^2} + \frac{n}{n^2 + 2^2} + \dots + \frac{n}{n^2 + 3^2 + \dots + \frac{1}{5n}} \right) =$
The right hand and left hand limit of the function are respectively
The value of $\displaystyle\lim_{x\to0} \frac{\left|x\right|}{x} $ is
The value of $\displaystyle\lim_{x \to 0} \frac {5^x-5^{-x}}{2x}=$ is :
\(\lim\limits_{n \to \infty} (\frac{n}{n^2+1^2}+\frac{n}{n^2+2^2}+\frac{n}{n^2+3^2}+…+\frac{1}{5n})=\)