List of top Mathematics Questions on Limits asked in BITSAT

Evaluate: \[ \lim_{x \to 0} \frac{\sin 3x - 3 \sin x}{x^3} \]

Let \( f(x) = \sin x \), \( g(x) = \cos x \), and \( h(x) = x^2 \). Then, evaluate: \[ \lim\limits_{x \to 1} \frac{f(g(h(x))) - f(g(h(1)))}{x - 1} \]

The value of $\displaystyle\lim_{n \to\infty} \frac{1+2+3+...n}{n^{2}+100}$ is equal to :

If $\sum\limits^{n}_{r=0} \frac{r+2}{r+1} \,^{n}C_{r} = \frac{2^{8}-1}{6} $, then $n =$

If a function $f(x)$ is given by $f(x)=\frac{x}{1+x}+\frac{x}{(x+1)(2 x+1)}+\frac{x}{(2 x+1)(3 x+1)}+\ldots \infty$ then at $x =0$, $f(x)$

If $f: R \rightarrow R$ is defined by $f(x)=[x-3]+|x-4|$ for $x \in R$, then $\displaystyle\lim _{x \rightarrow 3} f(x)$ is equal to

If $f : R \rightarrow R$ is defined by $f(x) = \begin{cases} \frac{\cos \ 3x - \cos \ x}{x^2} &, \text{for } x \neq 0 \\ \lambda &, \text{for } x = \end{cases}$ and if $f$ is continuous at $x = 0,$ then $\lambda$ is equal to

If $f(2) = 4$ and $f'(2) = 1$, then $\displaystyle\lim_{x \to 2} \frac{xf (2) - 2 f (x) }{x -2}$ is equal to