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

\[\lim_{x \to 4} \frac{x^3 - 64}{x^2 - 16}\] 

\[\lim_{x \to 1} \frac{x^{15} - 1}{x^{10} - 1}\] 

\[\lim_{x \to - 1} \frac{x^3 + 1}{x + 1}\] 

\[\lim_{x \to a} \frac{x^{2/3} - a^{2/3}}{x^{3/4} - a^{3/4}}\] 

If \[\lim_{x \to 3} \frac{x^n - 3^n}{x - 3} = 108,\]  find the value of n. 

If \[\lim_{x \to a} \frac{x^9 - a^9}{x - a} = 9,\] find all possible values of a. 

If \[\lim_{x \to a} \frac{x^5 - a^5}{x - a} = 405,\]find all possible values of a. 

If \[\lim_{x \to a} \frac{x^9 - a^9}{x - a} = \lim_{x \to 5} \left( 4 + x \right),\] find all possible values of a. 

If \[\lim_{x \to a} \frac{x^3 - a^3}{x - a} = \lim_{x \to 1} \frac{x^4 - 1}{x - 1},\] find all possible values of a. 

\[\lim_{x \to \infty} \frac{\left( 3x - 1 \right) \left( 4x - 2 \right)}{\left( x + 8 \right) \left( x - 1 \right)}\] 

\[\lim_{x \to \infty} \frac{3 x^3 - 4 x^2 + 6x - 1}{2 x^3 + x^2 - 5x + 7}\] 

\[\lim_{x \to \infty} \frac{5 x^3 - 6}{\sqrt{9 + 4 x^6}}\]

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

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

\[\lim_{x \to \infty} \sqrt{x^2 + 7x - x}\] 

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

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

\[\lim_{x \to \infty} \frac{3 x^{- 1} + 4 x^{- 2}}{5 x^{- 1} + 6 x^{- 2}}\]

\[\lim_{x \to \infty} \frac{\sqrt{x^2 + a^2} - \sqrt{x^2 + b^2}}{\sqrt{x^2 + c^2} - \sqrt{x^2 + d^2}}\] 

\[\lim_{n \to \infty} \left[ \frac{\left( n + 2 \right)! + \left( n + 1 \right)!}{\left( n + 2 \right)! - \left( n + 1 \right)!} \right]\]