What is the limit of #(x^4 + x^5) # as x approaches infinity?

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What is the limit of #(x^4 + x^5) # as x approaches infinity?

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Answer 1 · 2018-05-12T18:05:44

#\infty#

Explanation:

Write

#\lim_{x \rightarrow \infty} x^4 + x^5 = \lim_{x \rightarrow \infty} x^4 + \lim_{x \rightarrow \infty} x^5 = \infty + \infty = \infty#.
Or, you could think in this way. #x^5 +x^4# is a polynomial of degree 5. After the last root (the greater one), the function either increase or decrease without a bound. So the limit will always be #\infty# or #-\infty# depending on the sign

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What is the limit of #(x^4 + x^5) # as x approaches infinity?

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