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

\[\lim_{x \to 0^-} \frac{\sin \left[ x \right]}{\left[ x \right]} .\] 

\[\lim_{x \to \pi} \frac{\sin x}{x - \pi} .\] 

Write the value of \[\lim_{x \to \infty} \frac{\sin x}{x} .\] 

\[\lim_{x \to \infty} \left\{ \frac{3 x^2 + 1}{4 x^2 - 1} \right\}^\frac{x^3}{1 + x}\]

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

Write the value of \[\lim_{x \to 0^-} \left[ x \right] .\]

Write the value of \[\lim_{x \to 0^+} \left[ x \right] .\]

Write the value of \[\lim_{x \to 1^-} x - \left[ x \right] .\] 

Write the value of \[\lim_{x \to 0^-} \frac{\sin \left[ x \right]}{\left[ x \right]} .\]

Write the value of \[\lim_{x \to \pi} \frac{\sin x}{x - \pi} .\]

\[\lim_{x \to \infty} \frac{\sin x}{x} .\] 

Write the value of \[\lim_{x \to 2} \frac{\left| x - 2 \right|}{x - 2} .\] 

Write the value of \[\lim_{x \to 0} \frac{\sin x^\circ}{x} .\]

\[\lim_{x \to 0^-} \frac{\sin x}{\sqrt{x}} .\] 

\[\lim_{n \to \infty} \frac{1^2 + 2^2 + 3^2 + . . . + n^2}{n^3}\] 

\[\lim_{x \to 0} \frac{\sin 2x}{x}\] 

If \[f\left( x \right) = x \sin \left( 1/x \right), x \neq 0,\]  then \[\lim_{x \to 0} f\left( x \right) =\] 

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

\[\lim_{x \to 0}  \frac{\left( 1 - \cos 2x \right) \sin 5x}{x^2 \sin 3x} =\]

\[\lim_{x \to 0} \frac{x}{\tan x} is\]