High School

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Lim x → 3 f(x) = [infinity], lim x → [infinity] f(x) = −[infinity], lim x → −[infinity] f(x) = 0, lim x → 0 f(x) = −[infinity], lim x → 0− f(x) = [infinity]. (True or False)

Answer :

Final answer:

The given statements accurately describe the behavior of the function f(x) as x approaches specific values or infinity, making the answer true.

Explanation:

True. In this question, the given limits represent the behavior of the function f(x) as x approaches certain values or infinity. Let's analyze each limit individually:

  1. As x approaches 3, f(x) approaches infinity.
  2. As x approaches infinity, f(x) approaches negative infinity.
  3. As x approaches negative infinity, f(x) approaches 0.
  4. As x approaches 0, f(x) approaches negative infinity.
  5. As x approaches 0 from the left side (0-), f(x) approaches infinity.

The given statements accurately describe the behavior of the function f(x) as x approaches specific values or infinity, making the answer true.

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