Chapter 1.2, Problem 41ES

(a) Explain why the following calculation is incorrect.

$\underset{x\to 0^{+}}{\lim }\left(\frac{1}{x}-\frac{1}{x^2}\right)=\underset{x\to 0^{+}}{\lim }\frac{1}{x}-\underset{x\to 0^{+}}{\lim }\frac{1}{x^2}=+\infty -\left(+\infty \right)=0$

(b) Show that $\underset{x\to 0^{+}}{\lim }\left(\frac{1}{x}-\frac{1}{x^2}\right)=-\infty$ .