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?Prove that \(\lim \limits_{x \rightarrow 0^{+}} \ln x=-\infty\)
Chapter 2, Problem 43(choose chapter or problem)
QUESTION:
Prove that \(\lim \limits_{x \rightarrow 0^{+}} \ln x=-\infty\).
Questions & Answers
QUESTION:
Prove that \(\lim \limits_{x \rightarrow 0^{+}} \ln x=-\infty\).
ANSWER:Step 1 of 2
It is known that for every negative number N, there exists \(\delta>0\) such that \(0<|x-0|<\delta \Rightarrow f(x)<N\).
Let \(N<0\) be any real number. Observe that
\(f(x)<N \Leftrightarrow x=e^{\ln x}<e^{N}\)