Problem 2: For the following statements, say whether they are true or false. If true, provide a brief explanation. If false, provide a counterexample. (a) If f+g is continuous at c, and f is continuous at c, then g is continuous at c (b) If f.g is continuous at c, and f is continuous at c, then g is continuous at c. (c) If f is continuous with domain a bounded interval, then it has a minimum and a maximum. (d) If f is continuous with domain [0, 1] u [2, 3], then it has a minimum and a maximum. (e) If f(x)> 0 and limc f(x) exists, then lim+c f(x)> 0.

Question
Problem 2: For the following statements, say whether they are true or false. If true, provide a
brief explanation. If false, provide a counterexample.
(a) If f+g is continuous at c, and f is continuous at c, then g is continuous at c
(b) If f.g is continuous at c, and f is continuous at c, then g is continuous at c.
(c) If f is continuous with domain a bounded interval, then it has a minimum and a maximum.
(d) If f is continuous with domain [0, 1] u [2, 3], then it has a minimum and a maximum.
(e) If f(x)> 0 and limc f(x) exists, then lim+c f(x)> 0.
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Problem 2: For the following statements, say whether they are true or false. If true, provide a brief explanation. If false, provide a counterexample. (a) If f+g is continuous at c, and f is continuous at c, then g is continuous at c (b) If f.g is continuous at c, and f is continuous at c, then g is continuous at c. (c) If f is continuous with domain a bounded interval, then it has a minimum and a maximum. (d) If f is continuous with domain [0, 1] u [2, 3], then it has a minimum and a maximum. (e) If f(x)> 0 and limc f(x) exists, then lim+c f(x)> 0.

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