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either prove that it’s true by explicitly using limit laws, or give examples of functions that...

either prove that it’s true by explicitly using limit laws, or give examples of functions that contradict the statement

a) If limx→0 [f(x)g(x)] exists as a real number, then both limx→0 f(x) and limx→0 g(x) must exist as real numbers

b) If both limx→0 [f(x) − g(x)] and limx→0 f(x) exist as real numbers, then limx→0 g(x) must exist as a real number

Math   Calculus   
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