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4. Let f be a function with domain R. Is each of the following claims true...

4. Let f be a function with domain R. Is each of the following claims true or false? If it is false, show it with a counterexample. If it is true, prove it directly from the FORMAL DEFINITION of a limit.

(a) IF limx→∞ f(x) = ∞ THEN limx→∞ sin (f(x))  does not exist.

(b) IF f(−1) = 0 and f(1) = 2 THEN limx→∞ f(sin(x)) does not exist.

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