Which of the following function dominates the other one?
1) $f(x)= \log(x+1)$ and $g(x)= x$ as functions from $\mathbb N$ to $\mathbb N$.
2) $f(x)=2^x$ and $g(x)=1000000x$ as functions from $\mathbb Z$ to $\mathbb Z$.
2026-04-03 01:30:57.1775179857
Which one of the following functions dominates the other one?
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PLEASE USE THIS HINT: Consider two functions $f(x), g(x)$. The function $f(x)$ is said to dominate over $g(x)$ if $$\lim_{x\to \infty} \frac{g(x)}{f(x)} = 0$$ A simple application of this hint easily gives us the required answers. Hope it helps.