PUC Science कक्षा ११ - Karnataka Board PUC Question Bank Solutions for Mathematics

\[\lim_{x \to 0} \frac{\tan mx}{\tan nx}\] 

\[\lim_{x \to 0} \frac{\sin 5x}{\tan 3x}\] 

\[\lim_{x \to 0} \frac{\sin x^n}{x^n}\] 

\[\lim_{x \to 0} \frac{7x \cos x - 3 \sin x}{4x + \tan x}\] 

\[\lim_{x \to 0} \frac{\cos ax - \cos bx}{\cos cx - \cos dx}\] 

\[\lim_{x \to 0} \frac{\tan^2 3x}{x^2}\] 

\[\lim_{x \to 0} \frac{1 - \cos mx}{x^2}\] 

\[\lim_{x \to 0} \frac{3 \sin 2x + 2x}{3x + 2 \tan 3x}\] 

\[\lim_{x \to 0} \frac{\cos 3x - \cos 7x}{x^2}\] 

\[\lim_\theta \to 0 \frac{\sin 3\theta}{\tan 2\theta}\] 

\[\lim_{x \to 0} \frac{\sin x^2 \left( 1 - \cos x^2 \right)}{x^6}\] 

\[\lim_{x \to 0} \frac{\sin^2 4 x^2}{x^4}\] 

\[\lim_{x \to 0} \frac{x \cos x + 2 \sin x}{x^2 + \tan x}\] 

\[\lim_{x \to 0} \frac{2x - \sin x}{\tan x + x}\] 

\[\lim_{x \to 0} \frac{5 x \cos x + 3 \sin x}{3 x^2 + \tan x}\] 

\[\lim_{x \to 0} \frac{\sin 3x - \sin x}{\sin x}\] 

\[\lim_{x \to 0} \frac{\sin 5x - \sin 3x}{\sin x}\] 

\[\lim_{x \to 0} \frac{\tan 3x - 2x}{3x - \sin^2 x}\] 

\[\lim_{x \to 0} \frac{\sin \left( 2 + x \right) - \sin \left( 2 - x \right)}{x}\]

\[\lim_{h \to 0} \frac{\left( a + h \right)^2 \sin \left( a + h \right) - a^2 \sin a}{h}\]