Chapter 2 - Section 2.2 - The Limit of a Function - 2.2 Exercises - Page 94: 43

$\lim\limits_{x \to 0}(ln~x^2-x^{-2}) = -\infty$

$\lim\limits_{x \to 0}(ln~x^2-x^{-2})$ When $x$ is close to 0, $x^2$ is a very small positive number. Then $ln~x^2$ approaches $-\infty$ The value of $x^{-2} = \frac{1}{x^2}$ approaches $\infty$ Then, the value of $(ln~x^2-x^{-2})$ approaches $-\infty$