Formula used:\(\lim\limits_{x \to 0}\frac{sin \ x}{x} = 1\)\(cosec\ x=\frac{1}{sin\ x}\)Calculation:Let the required value be y.? y = \(\lim\limits_{x \to 0}x^3(\text{cosec} \ x)^2\)? y = \(\lim\limits_{x \to 0}\frac{x^3}{(sin \ x)^2}\)? y = \(\lim\limits_{x \to 0}(\frac{x}{sin \ x})^3sin\ x\)We know that, \(\lim\limits_{x \to 0}\frac{sin \ x}{x} = 1\)? y = \(\lim\limits_{x \to 0}sin\ x\)Taking the limit ? y = 0? \(\lim\limits_{x \to 0}x^3(\text{cosec} \ x)^2\) = 0