Show that 2n is O(3n) but not that 3n is not O(2n)

Name: Show that 2n is O(3n) but not that 3n is not O(2n)
Uploaded: 2024-03-20T06:38:58.000Z
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Description: Show that 2n is O(3n) but not that 3n is not O(2n)

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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Show that 2ⁿ is O(3ⁿ) but not that 3ⁿ is not O(2ⁿ)

Expert Solution

Step 1

We need to show that $2^{n} i s O (3^{n}) b u t 3^{n} i s n o t O (2^{n})$

Definition of Big O notation:

Let f be a real valued or a complex function and g be a real valued function.

Let us assume that f and g are defined on unbounded subset of real numbers and g(x) be strictly positive for large values of x.

Then we can say that $f (x) = O (g (x))$ as $x \to \infty$ if $|f (x)| \leq M g (x) f o r a l l x \geq x_{0}$

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