List of top Mathematics Questions on limits of trigonometric functions asked in KEAM

The value of $\lim_{x \to 0} \dfrac{\sqrt{1 - \cos(x^2)}}{1 - \cos x}$ is equal to:

The value of $\lim_{x \to 0} \dfrac{\sin^2 x}{1 - \cos x}$ is equal to:

$\lim_{x\rightarrow0}\frac{\sin(\pi \sin^{2}x)}{x^{2}} = $ ________.

The value of $\lim\limits_{x \to 0} \frac{(x-\sin 2x)(2x-\sin x)}{x^2}$ is equal to:

$\lim_{x\rightarrow 2}\frac{\sin x \cos 2 - \cos x \sin 2}{x-2} =$

$\lim_{\theta\rightarrow 0}\frac{\theta \sin 2\theta}{1-\cos 2\theta} =$

$\lim_{x\rightarrow 0}\frac{\sin x}{2\sqrt{2}\sin\frac{x}{\sqrt{2}}} =$

$\displaystyle\lim_{x \to 0}\frac{1 - \cos 4x}{\tan^2 2x}$ is equal to

\( \lim_{x \to 0} \frac{1 - \cos(mx)}{1 - \cos(nx)} \) is

\( \lim_{x \to 0} \frac{1 - \cos(mx)}{1 - \cos(nx)} \) is

\( \lim_{x \to 0} \frac{1 - \cos(mx)}{1 - \cos(nx)} \) is

\( \lim_{x \to 0} \frac{1 - \cos(mx)}{1 - \cos(nx)} \) is

The value of $\lim_{x \to 0} \frac{\cot 4x}{\csc 3x}$ is equal to:

\[ \lim_{x \to 0} \left(\frac{10\sin 9x}{9\sin 10x}\right) \left(\frac{8\sin 7x}{7\sin 8x}\right) \left(\frac{6\sin 5x}{5\sin 6x}\right) \left(\frac{4\sin 3x}{3\sin 4x}\right) \left(\frac{\sin x}{\sin 2x}\right) \]