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Let f: R → [0,∞) be a function for which the limit lim_(x→5) f(x) exists, and also lim_(x→5) ((f(x))² - 9)/(√(|x-5|)) = 0. Then the value of lim_(x→5) f(x) is:

1. 0
2. 1
3. 2
4. 3

Correct answer: 3

Solution

The limit condition indicates that as x approaches 5, the expression (f(x))² approaches 9, which implies that f(x) approaches either 3 or -3. However, since f(x) is constrained to be non-negative (f: R → [0,∞)), the only feasible limit is 3.

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