Math  /  Calculus

Question1. limxcf(x)=f(c)\lim _{x \rightarrow c} f(x)=f(c) II. f(c)f(c) is defined
III limxcf(x)\lim _{x \rightarrow c} f(x) must exist a. True b. false

Studdy Solution
Combine the three conditions to determine if the overall statement holds.
For f(x) f(x) to be continuous at c c :
1. f(c) f(c) must be defined.
2. limxcf(x) \lim_{x \to c} f(x) must exist.
3. limxcf(x)=f(c) \lim_{x \to c} f(x) = f(c) .

Since the given statements I, II, and III are exactly the conditions required for continuity, the overall statement is:
a. True
Solution: The correct answer is a. True \text{a. True} .

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