$\lim_{x \to 0} \left( \frac{x^2 \sin^2 x}{x^2 - \sin^2 x} \right)$ का मान है:

$\mathop {\lim }\limits_{x \to \infty } {\left( {\frac{{{x^2} + 5x + 3}}{{{x^2} + x + 3}}} \right)^x} = $

$\mathop {\lim }\limits_{x \to 0} \frac{x}{|x| + {x^2}} = $

$\mathop {\lim }\limits_{n \to \infty } {\left( {\frac{{{n^2} - n + 1}}{{{n^2} - n - 1}}} \right)^{n(n - 1)}} = $

यदि $f(x) = \begin{cases} x, & \text{जब } 0 \le x \le 1 \\ 2 - x, & \text{जब } 1 < x \le 2 \end{cases}$,तो $\lim_{x \to 1} f(x) = $

$\mathop {\lim }\limits_{n \to \infty } \left( \frac{1}{2} + \frac{1}{{{2^2}}} + \frac{1}{{{2^3}}} + ... + \frac{1}{{{2^n}}} \right)$ का मान ज्ञात कीजिए।