Limit of lnx as x approaches Infinity (with Mean Value Theorem) | Real Analysis Exercises

We prove the limit of ln(x) as x goes to infinity is infinity. To do this we use the Mean Value Theorem for definite integrals to show that ln(2) is at least 1/2, then we will take x to be greater than 2^(2M) for a fixed M greater than 0. This will quickly lead to the desired inequality, that ln x is greater than M. #RealAnalysis

Mean Value Theorem for Definite Integrals: (coming soon)


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[wonbpoly]

thank you for this every teacher around the world should teach like this, god blessed you sir.

[winminaye]

we also need graph theory problems and theorem explanation. Thanks a lot!!

[rosyy]

nice proof tho my textbook says ln x > 2k ln2> 2k(1/2)=k :( but I dont think its correct and im using Schaum's