Explain what it means to say that lim f x 8 and X 3 X 3 O As x approaches 3 from the right f x approaches 8 As x approaches 3

Question

Explain what it means to say that lim f x 8 and X 3 X 3 O As x approaches 3 from the right f x approaches 8 As x approaches 3 from the left f x approaches 5 O As x approaches 3 from the left f x approaches 8 As x approaches 3 from the right f x approaches 5 O As x approaches 3 f x approaches 5 but f 3 8 O As x approaches 3 f x approaches 8 but f 3 5 lim f x 5 In this situation is it possible that lim f x exists Explain X 3 O Yes f x could have a hole at 3 8 and be defined such that f 3 5 O Yes f x could have a hole at 3 5 and be defined such that f 3 8 Yes if f x has a vertical asymptote at x 3 it can be defined such that lim f x 8 lim f x 5 and lim f x exists X 3 X 3 X 3 No lim f x cannot exist if lim f x lim f x X 3

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