Answer Happy

Explain the meaning of the following equation. x→2lim​f(x)=6 The values of f(x) can be made as close to 2 as we like by taking x sufficiently close to 6 . The values of f(x) can be made as close to 6 as we like by taking x sufficiently close to 2 . f(x)=6 for all values of x. If ∣x1​−2∣<∣x2​−2∣, then ∣f(x1​)−6∣<∣f(x2​)−6∣. If ∣x1​−2∣<∣x2​−2∣, then ∣f(x1​)−6∣≤∣f(x2​)−6∣. Is it possible for this statement to be true and yet f(2)=8 ? Explain. Yes, the graph could have a hole at (2,6) and be defined such that f(2)=8. Yes, the graph could have a vertical asymptote at x=2 and be defined such that f(2)=8. No, if f(2)=8, then x→2lim​f(x)=8. No, if x→2lim​f(x)=6, then f(2)=6.