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Comparing growth rates Determine which of the

Chapter 4, Problem 48RE

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QUESTION:

Determine which of the two functions grows faster, or state that they have comparable growth rates.

\(\sqrt{x^6+10}\ and\ x^3\)

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QUESTION:

Determine which of the two functions grows faster, or state that they have comparable growth rates.

\(\sqrt{x^6+10}\ and\ x^3\)

ANSWER:

Solution Step 1 x In this problem we have to determine which of the two functions e and 3 , grows faster than the other otherwise we have to state the comparable growth rates. Suppose f and gare functions such that limf(x) = , limg(x) = x x f(x) Enough to prove:lim g(x)= 0which means ggrows faster than f as x x

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