Mathematics

Mathematics

Problem

Consider a function ff whose graph behaves as follows near x=1x=1: • For xx values just less than 11, f(x)f(x) is very close to 22. • For xx values just greater than 11, f(x)f(x) is very close to 44. (i) Find lim⁡x→1−f(x)\displaystyle\lim_{x\to1^-}f(x). (ii) Find lim⁡x→1+f(x)\displaystyle\lim_{x\to1^+}f(x). (iii) Does lim⁡x→1f(x)\displaystyle\lim_{x\to1}f(x) exist? Give one reason for your answer. a. (i) lim⁡x→1−f(x)\displaystyle\lim_{x\to1^-}f(x) b. (ii) lim⁡x→1+f(x)\displaystyle\lim_{x\to1^+}f(x) c. (iii) Existence of lim⁡x→1f(x)\displaystyle\lim_{x\to1}f(x) with reason

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