5. For each of the following statements, either prove it or disprove it by giving a counterexample. (a) If lim f(z), lim g(z) both exist and f(x) > g(x) for allz ER, then lim f(x) > lim g(z). (b) If f: (a, b) R is a continuous function, then there exists c e (a, b) such that f(c) 2 f(=) for all z E (a, b). (c) If f(x) is an odd, differentiable function, then f'(z) is an even function. (d) If f : [a, b) -R is a continuous function such that f(z) > 0 for all a € (a, 6), them | (=) dz > 0.

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A: This question can be solved using the definition of increasing function.

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A: To evaluate the indicated limits:

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A: Given that : as per squeeze theorem

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A:

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Q: Consider the following graph of f(z). 10 -9 -6 a m co 8 6- + 2- b N T -6 -m 3 -60 9 a For 12 X

A: