Question
Prove that $$ \displaystyle \lim_{x\to \infty} \frac{\ln x}{x^p} = 0 $$for any number $ p > 0 $. This shows that the logarithmic function approaches infinity more slowly than any power of $ x $.
Step 1
Step 1: We start with the given limit: $$ \lim_{x\to \infty} \frac{\ln x}{x^p} $$ Show more…
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