List of top Mathematics Questions on Limits asked in Guru Gobind Singh Indraprastha University Common Entrance Test

Evaluate the limit: lim⁡x→01−cos⁡4x2sin⁡2x+xtan⁡7x \lim_{x \to 0} \frac{1 - \cos 4x}{2 \sin^2 x + x \tan 7x}
Choose the most appropriate option. lim⁡x→1x(1−x)\lim_{x \to 1} x^{(1-x)} is equal to:
lim⁡x→∞ln⁡xxn\lim_{x \to \infty} \frac{\ln x}{x^n} is equal to
lim⁡x→0ax−1x is equal to \lim_{x \to 0} \frac{a^x - 1}{x} \text{ is equal to}
lim⁡x→0tan⁡−1(−x1−x2)ln⁡(1−x)=? \lim_{x \to 0} \frac{\tan^{-1} \left( \frac{-x}{\sqrt{1 - x^2}} \right)}{\ln(1 - x)} = ?
If i=−1i = \sqrt{-1}, then lim⁡n→∞(n+2i)(3+7in)(2−i)(6n2+1) \lim_{n \to \infty} \frac{(n + 2i)(3 + 7in)}{(2 - i)(6n^2 + 1)} is equal to:
lim⁡x→π/4(1−cos⁡x)2tan⁡2x−sin⁡2x is equal to: \lim_{x \to \pi/4} \frac{(1 - \cos x)^2}{\tan^2 x - \sin^2 x} \text{ is equal to:}
Choose the most appropriate options.
The period of the function f(x)=∣sin⁡x∣−∣cos⁡x∣f(x) = |\sin x| - |\cos x| is