List of top Mathematics Questions on Limits asked in MHT CET

$\lim_{x \to 0} \frac{63^x - 9^x - 7^x + 1}{\sqrt{2} - \sqrt{1 + \cos x}} = \dots$

$\lim_{x \to \infty} \frac{(2x+1)^{50} + (2x+2)^{50} + (2x+3)^{50} + \dots + (2x+100)^{50}}{(2x)^{50} + (10)^{50}} = $ ______.

$\lim_{x\rightarrow0}\frac{e^{x^{2}}-\cos 3x}{\sin x \log(1+2x)}=$

The area of a parallelogram whose diagonals are the vectors \(2\bar{a} - \bar{b}\) and \(4\bar{a} - 5\bar{b}\), where \(\bar{a}\) and \(\bar{b}\) are unit vectors forming an angle of \(45^\circ\) is

Evaluate the limit $ \lim_{n \to \infty} \frac{6^n - 9x - 7^n + 1}{\sqrt{2} - \sqrt{11} + \cos n} $

Evaluate the limit: $\lim_{x \to 1} \left[ \frac{\sqrt{x} - 1}{\log x} \right] =$

$\lim_{x \rightarrow 1} \frac{ab^x - a^x b}{x^2 - 1} = $

$\lim _{x \rightarrow 1} \frac{(2 x-3)(\sqrt{x}-1)}{2 x^2+x-3}=$

If \[ \lim_{x \to 5} \frac{x^k - 5^k}{x - 5} = 500 \], then the value of \( k \), where \( k \in \mathbb{N} \) is

If $a = \lim_{n \rightarrow \infty} \frac{1+2+3+\ldots+n}{n^2}$ and $b = \lim_{n \rightarrow \infty} \frac{1^2+2^2+3^2+\ldots+n^2}{n^3}$, then

$\lim_{x \to \infty} \left( \sqrt{x^2 + 5x - 7} - x \right) =$

$\lim _{x \rightarrow 1} \frac{(2 x-3)(\sqrt{x}-1)}{2 x^2+x-3}=$