$\mathop {\lim }\limits_{x \to 0} \cos \frac{1}{x}$

લક્ષની કિંમત શોધો: $\mathop {\lim }\limits_{x \to \infty } [x({a^{1/x}} - 1)]$,જ્યાં $a > 1$.

$\mathop {\lim}\limits_{x \to 1} \left[ {\left[ {\frac{4}{{{x^2} - {x^{ - 1}}}} - \frac{{1 - 3x + {x^2}}}{{1 - {x^3}}}} \right]^{ - 1} + \frac{{3 \cdot ({x^4} - 1)}}{{{x^3} - {x^{ - 1}}}}} \right] = $

$\lim _{x \rightarrow 0}(1+3x)^{\frac{2}{x}} = $

$\mathop {\lim }\limits_{m \to \infty } {\left( {\cos \frac{x}{m}} \right)^m} = $

$\lim_{x \to 0} \left( \frac{x^2 \sin^2 x}{x^2 - \sin^2 x} \right)$ નું મૂલ્ય શું છે?