List of top Mathematics Questions on Limits asked in IPU CET

Choose the most appropriate option. \(\lim_{x \to 1} x^{(1-x)}\) is equal to:

Evaluate the limit: \[ \lim_{x \to 0} \frac{1 - \cos 4x}{2 \sin^2 x + x \tan 7x} \]

Choose the most appropriate options.
The period of the function \(f(x) = |\sin x| - |\cos x|\) is

$\lim_{x \to 0} \frac{\tan^{-1} \left( \frac{-x}{\sqrt{1 - x^2}} \right)}{\ln(1 - x)} =\ ?$

\(\lim_{x \to \infty} \frac{\ln x}{x^n}\) is equal to

If \(i = \sqrt{-1}\), then \[ \lim_{n \to \infty} \frac{(n + 2i)(3 + 7in)}{(2 - i)(6n^2 + 1)} \] is equal to:

\[ \lim_{x \to \pi/4} \frac{(1 - \cos x)^2}{\tan^2 x - \sin^2 x} \text{ is equal to:} \]