EXAMPLE 7Finding the Limit at Infinity of f(x)=lnx
Find lim.
Figure 60 f(x)=\ln x
Solution Table 17 and the graph of f( x) =\ln x in Figure 60 suggest that \ln x has an infinite limit at infinity. That is, \bbox[5px, border:1px solid black, #F9F7ED]{\lim\limits_{x\rightarrow \infty }\ln x =\infty}
| x | e^{10} | e^{100} | e^{1000} | e^{10{,}000} | e^{100{,}000} | \rightarrow x becomes unbounded |
| f( x) =\ln x | 10 | 100 | 1000 | 10,000 | 100,000 | \rightarrow f(x) becomes unbounded |