Answer to Question #157289 in Calculus for Vishal

Question #157289

Prove that the set A given by A:={2020/n +n² : n∈N} is unbounded above.


1
Expert's answer
2021-01-26T18:49:59-0500

A function is bounded above if there is a real number, k, such that for all of xf(x) ≤ k.

The number k is called the upper bound.

because A=2020/n+n2, and

if "\\lim _{n \\rightarrow \\infty} n^{2}+\\frac{2020}{n}" =infinity, it means k equals to infinity and A is unbounded above.

"\\lim _{n \\rightarrow \\infty} n^{2}+\\frac{2020}{n}" = "\\lim _{n \\rightarrow \\infty}" ("\\infty")2+0="\\infty", so the set A is unbounded above


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