Investigating an Infinite Limit

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

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 \[\bbox[5px, border:1px solid black, #F9F7ED]{\lim\limits_{x\rightarrow 0^{+}}\ln x=-\infty} \]