Consider the function below.

lim x -> 3 x^2=9
What values of x guarantee that f(x) = x^2 is within 0.62 units of 9?
If x is within _____ units of 3, then f(x) is within 0.62 units of 9.
in Calculus Answers by Level 1 User (940 points)

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1 Answer

Let x=3±h where h is small.

f(3±h)=(3±h)²=9±6h+h²=9±0.62, so ±6h≈0.62 if we ignore h² as being insignificantly small.

So h=0.62/6=0.10 approx.

If x is within 0.10 units of 3, then f(x) is within 0.62 units of 9.

by Top Rated User (628k points)

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