Chapter 14 - A Preview of Calculus: The Limit, Derivative, and Integral of a Function - 14.2 Algebra Techniques for Finding Limits - 14.2 Assess Your Understanding - Page 884: 56

$1$

$$\lim_{x\to 0}\frac{\sin^2{x}+\sin{x}(\cos{x}-1)}{x^2}\\=\lim_{x\to 0}\frac{\sin^2{x}}{x^2}+\lim_{x\to 0}\frac{\sin{x}(\cos{x}-1)}{x^2}\\=\lim_{x\to 0}(\frac{\sin{x}}{x})^2+(\lim_{x\to 0}\frac{\sin{x}}{x}\frac{\cos{x}-1}{x})\\=1^2+1(0)\\=1.$$