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Mathematics LibreTexts

4.E: Exercises

  • Page ID
    18549
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    4.1: Big-O Notation

    1. Show that \(f(x)=\frac{x^3-2x+4}{50x^2-3}\) is \(O(x)\).

    2. Prove or disprove: \(3^{2n}\) is \(O(3^n)\).

    3. Prove part 2 of Theorem 4.1.6.

    4.2: Some Algorithms

    1. This website provides an algorithm to multiply two numbers together. Suppose each number has \(n\) digits. Find a big-O estimate of the time complexity of this algorithm.