Investigate $\lim\limits_{x\rightarrow 0^{+}}\ln x$.

Figure 49 $f(x)=\ln x$

Solution The domain of $f(x)=\ln x$ is $\{x|x>0\}$. Notice that the graph of $f(x)=\ln x$ in Figure 49 decreases without bound as $x$ approaches $0$ from the right. The graph suggests that $$\bbox[5px, border:1px solid black, #F9F7ED]{\lim\limits_{x\rightarrow 0^{+}}\ln x=-\infty}$$