SOLUTION: 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 ____

SOLUTION: 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 u

Question 1120559: 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.
Answer by greenestamps(13203) (Show Source): You can put this solution on YOUR website!

We need to have

(9-0.62) < x^2 < (9+0.62)
sqrt(8.38) < x < sqrt(9.62)
2.8948 < x < 3.1016 (approximately)

The upper limit is closer to 3 (3.1016-3 = 0.1016) than the lower limit (3-2.8948 = 0.1052). So to guarantee that x^2 is within 0.62 of 9, x has to be within approximately 0.1052 of 3.
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