Chapter 2 - Section 2.2 - The Limit of a Function - 2.2 Exercises - Page 94: 42

$\lim\limits_{x \to 0^+}(\frac{1}{x}-ln~x) = \infty$

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