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Let $\lim _{n \rightarrow \infty} f(n)=\infty$ and $\lim _{n \rightarrow \infty} g(n)=\infty$. Then which of the following is necessarily $\text{TRUE.}$

  1. $\lim _{n \rightarrow \infty}|f(n)-g(n)|=\infty$
  2. $\lim _{n \rightarrow \infty}|f(n)-g(n)|=0$
  3. $\lim _{n \rightarrow \infty}|f(n) / g(n)|=\infty$
  4. $\lim _{n \rightarrow \infty}|f(n) / g(n)|=1$
  5. None of the above 

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