PUC Science इयत्ता ११ - Karnataka Board PUC Question Bank Solutions

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 \[\lim_{x \to 0} f\left( x \right) =\] 

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

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

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

\[\lim_{n \to \infty} \left\{ \frac{1}{1 - n^2} + \frac{2}{1 - n^2} + . . . + \frac{n}{1 - n^2} \right\}\]

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

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

\[\lim_{x \to 3} \frac{x - 3}{\left| x - 3 \right|},\] is equal to

\[\lim_{x \to a} \frac{x^n - a^n}{x - a}\]  is equal at 

\[\lim_{x \to \pi/4} \frac{\sqrt{2} \cos x - 1}{\cot x - 1}\] is equal to

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

\[\lim 2_{h \to 0} \left\{ \frac{\sqrt{3} \sin \left( \pi/6 + h \right) - \cos \left( \pi/6 + h \right)}{\sqrt{3} h \left( \sqrt{3} \cos h - \sin h \right)} \right\}\]