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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Q: last two subparts

A: To determine the validity of 2d) and 2e)

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A: As image of a connected set is connected in of every continuous function.

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A: Given that n is a positive integer and f(x)=(x)^1/n.

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Q: If f(x) = then f (x) at z = 1 is

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Q: ⎪ ⎨ ⎪ ⎧x^2 − 1 , − 1 ≤ x < 0 2x , 0 < x < 1 1 , x = 1 −2x + 4 , 1 < x < 2 0 , 2 < x < 3 a) Is f…

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