List of top Mathematics Questions on limits and derivatives asked in MET

The value of \( \lim_{x \to 0} \left(\frac{e^x + 2^x + 4^x}{3}\right)^{\frac{2}{x}} \) is:
\(\lim_{x \to 2} \frac{2 - \sqrt{2 + x}}{2^{1/3} - (4 - x)^{1/3}}\) is equal to
If \[ \lim_{x \to 0} \frac{\sin(\sin x) - \sin x}{ax^3 + bx^5 + c} = -\frac{1}{12}, \] then
If \( f(x) = \begin{cases} \frac{\sin |x|}{x}, & \text{for } [x] \ne 0 \\ 0, & \text{for } [x] = 0 \end{cases} \) where, \([x]\) denotes the greatest integer less than or equal to \(x\), then \(\lim_{x \to 0} f(x)\) is equal to
\( \lim_{x \to \infty} \left(\frac{x+5}{x+2}\right)^{x+3} \) equals
The value of \( \lim_{n \to \infty} \frac{1 + 2 + 3 + \dots + n}{n^{2}} \) is: