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

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

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

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

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

\[\lim_{x \to 0} \frac{1 - \cos 2x}{\cos 2x - \cos 8x}\]

\[\lim_{x \to 0} \frac{1 - \cos 2x + \tan^2 x}{x \sin x}\] 

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

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

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

\[\lim_{x \to 0} \frac{x \tan x}{1 - \cos x}\]

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

\[\lim_{x \to 0} \frac{\sin 2x \left( \cos 3x - \cos x \right)}{x^3}\] 

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

\[\lim_{x \to 0} \frac{x^3 \cot x}{1 - \cos x}\] 

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

\[\lim_{x \to 0} \frac{\sin \left( 3 + x \right) - \sin \left( 3 - x \right)}{x}\] 

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

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

\[\lim_{x \to 0} \frac{\sqrt{1 + \sin x} - \sqrt{1 - \sin x}}{x}\] 

\[\lim_{x \to 0} \frac{1 - \cos 4x}{x^2}\]