# 4.E: Exercises

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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.

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