Limits of Trigonometric Functions

Evaluate $\underset{x\to 0}{\lim } \frac{\sqrt{7}-\sqrt{6+\cos x}}{x\sin x}$

Evaluate $\underset{x\to 0}{\lim }\frac{\cos 2x-1}{\cos x-1}$.

Evaluate: $\underset{x\to 0}{\lim }\frac{\sin ax+bx}{ax+\sin bx}$ where $a,b,a+b\ne 0$

Find the value of $\underset{x\to 0}{\lim }\frac{\sin 3x}{x}$

$\underset{x\to 0}{\lim }\frac{\sin x}{\sqrt{x}}$ is _____

Evaluate: $\underset{x\to 0}{\lim }\frac{{\sin }^{-1}x}{\sin x}$

Evaluate $\underset{x\to 0}{\lim }\frac{\cos 2x-1}{\cos x-1}$.

Evaluate $\underset{\mathrm{x}\to \mathrm{a}}{\lim }\frac{{\mathit{x}}^{{\displaystyle \frac{3}{2}}}\mathit{-}{\mathit{a}}^{{\displaystyle \frac{3}{2}}}}{\mathit{x}\mathit{-}\mathit{a}}$

Evaluate: $\underset{x\to 0}{\lim }\frac{\sin ax+bx}{ax+\sin bx}$ where $a,b,a+b\ne 0$

Evaluate: $\underset{x\to 0}{\lim }\frac{x}{{\sin }^{-1}x}$

If $\mathrm{\alpha } \mathrm{and} \mathrm{\beta }$ be the roots of the equation ${\mathrm{ax}}^2+\mathrm{bx}+\mathrm{c}=0$ then $\underset{x\to \frac{1}{\alpha }}{\lim }\sqrt{\frac{1-\cos \left(c{x}^2+bx+a\right)}{2(1-\alpha x{)}^2}}$

Prove that $\underset{x\to 0}{\lim }\frac{\sin x°}{x}=\frac{{\displaystyle \mathrm{\pi }}}{180}$

Value of limit,

$\underset{x\to \frac{\mathrm{\pi }}{2}}{\lim }\frac{4\sqrt{2}\left(\sin 3x+\sin x\right)}{\left(2\sin 2x\sin {\displaystyle \frac{3x}{2}}+\cos {\displaystyle \frac{5x}{2}}\right)-\left(\sqrt{2}+\sqrt{2}\cos 2x+\cos {\displaystyle \frac{3x}{2}}\right)}$

The value of $\underset{x\to 0}{\lim }\frac{2\cos x-\cos 3x-\cos 5x}{x^2}$ is equal to

Find $\underset{x\to 0}{\lim }\frac{{\sin }^{2}4x}{x^2}$

Evaluate:

$\underset{x\to 0}{\lim }\frac{\tan x}{x}$

Evaluate $\underset{\theta \to 0}{\lim }\frac{\sin a\theta +b\theta }{a\theta +\sin b\theta }$.

Evaluate $\underset{x\to 0}{\lim }\frac{1-\cos x}{1-\cos 3x}$.

$\underset{x\to 0}{\lim }\frac{\sin x^2(1-\cos x^2)}{x^6}$

Find $\underset{x\to 0}{\lim }\frac{\cos ax-\cos bx}{x^2}$