Proof Prove that if and then
Chapter 8, Problem 108(choose chapter or problem)
FOR FURTHER INFORMATION For a geometric approach to this exercise,see the article “A Geometric Proof of \(\lim _{d \rightarrow 0^{+}}(-d \ln d)=0\)” by John H. Mathews in The College Mathematics Journal.To view this article,go to MathArticles.com.
Proof Prove that if \(f(x) \geq 0\), \(\lim _{x \rightarrow a} f(x)=0\), and \(\lim _{x \rightarrow a} g(x)=\infinity\), then \(\lim _{x \rightarrow a} f(x)^{g(x)}=0\)
Text Transcription:
lim_d rightarrow 0^+ (-d \ln d)=0
f(x) geq 0
lim_x rightarrow f(x)=0
lim_x rightarrow f(x)=infinity
lim_x rightarrow f(x)^g(x) = 0
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