Logarithm Tends to Infinity/Proof 2
Jump to navigation
Jump to search
Theorem
- $\ln x \to +\infty$ as $x \to +\infty$
Proof
From the definition of the natural logarithm:
\(\ds \ln x\) | \(=\) | \(\ds \int_1^x \dfrac 1 t \rd t\) |
The result follows from Integral of Reciprocal is Divergent.
$\blacksquare$
Sources
- 2005: Roland E. Larson, Robert P. Hostetler and Bruce H. Edwards: Calculus (8th ed.): Appendix $A$: Properties of the Natural Logarithmic Function