(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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