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

Let f(x)=x^m, m being a non-negative integer. The value of m so that the equality f'(a+b)=f'(a)+f'(b) is valid for all a,b>0 is

It $\displaystyle \lim_{x \to 0}$$\frac{axe^{x}-b\, \log\left(1+x\right)}{x^{2}}=3$ then the values of $a, b$ are respectively

Let $x_{n}=\left(1-\frac{1}{3}\right)^{2}\left(1-\frac{1}{6}\right)^{2}\left(1-\frac{1}{10}\right)^{2} ........ \left(1-\frac{1}{\frac{n\left(n+1\right)}{2}}\right)^2, n \ge 2.$ Then the value of $\displaystyle \lim_{n \to \infty} x_n$ is

The limit of $ \sum\limits^{1000}_{ n-1} (-1)^n \, x^n $ as $x?8$

$\displaystyle\lim _{x \rightarrow 0} \frac{\sin |x|}{x}$ is equal to

If $f(5)=7$ and $f^{'}(5)=7$ then $\displaystyle\lim _{x \rightarrow 5} \frac{x f(5)-5 f(x)}{x-5}$ is given by

Let [x] denote the greatest integer less than or equal to x. If f(x) = [x sinπ x], then f(x) is

Let f(x) = x³e^–3x, x  ^gt 0. Then the maximum value of f(x) is 

Directions: The following question has four choices, out of which one or more are correct.The equations of two ellipses are $\frac{x^2}{p^2}+y^2=1$ and $x^2+\frac{y^2}{p^2}=1,=1,$ where $p$ is a parameter. The locus of the points of intersection of both the ellipses is a set of curves comprising

The sum of n terms of an AP is n² + n; the common difference will be:

$\mathrm{f}\mathrm{A}+\mathrm{B}+\mathrm{C}=,$ then $\tan \left(\frac{\mathrm{A}}{2}\right)\tan \left(\frac{\mathrm{B}}{2}\right)+\tan \left(\frac{\mathrm{B}}{2}\right)\tan \left(\frac{\mathrm{C}}{2}\right)+\tan \left(\frac{\mathrm{C}}{2}\right)\tan \left(\frac{\mathrm{A}}{2}\right)$ is equal to