(Requires calculus) Show that if c > b > 1. then bn is
Chapter 2, Problem 60E(choose chapter or problem)
(Requires calculus) Show that if \(c>b>1\), then \(b^{n}\) is \(O\left(c^{n}\right)\) but \(c^{n}\) is not \(O\left(b^{n}\right)\).
The following problems deal with another type of asymptotic notation, called little-o notation. Because little-o notation is based on the concept of limits, a knowledge of calculus is needed for these problems. We say that \(f(x)\) is \(o(g(x))\) [read \(f(x)\) is "little-oh" of \(g(x)\) ], when
\(\lim _{x \rightarrow \infty} \frac{f(x)}{g(x)}=0\)
Equation Transcription:
Text Transcription:
c > b > 1
b^n
O(c^n)
c^n
O(b^n)
f(x)
o(g(x))
g(x)
Lim_x right arrow infinity f(x)/g(x) = 0
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