Chapter 1 - Limits and Continuity - 1.2 Computing Limits - Exercises Set 1.2 - Page 70: 42

$ \frac{1}{2}$

a. Multiplying $\infty$ by $0$ is an invalid operation. b. $\lim_{x \to 0} (\frac{1}{x} - \frac{2}{x^2+2x} ) = \lim_{x \to 0} (\frac{x^2+2x-2x}{x(x^2+2x)}) = \lim_{x \to 0} (\frac{x^2}{x^2(x+2)}) = \lim_{x \to 0} (\frac{1}{(x+2)}) = \frac{1}{2}$