Mathematics

Mathematics

Problem

For a function ff, it is known that lim⁡x→a−f(x)=2\displaystyle \lim_{x\to a^-}f(x)=2 and lim⁡x→a+f(x)=5\displaystyle \lim_{x\to a^+}f(x)=5. Which statement is necessarily true? a) ff is continuous at x=ax=a b) lim⁡x→af(x)\displaystyle \lim_{x\to a}f(x) does not exist because the one–sided limits are unequal c) lim⁡x→af(x)\displaystyle \lim_{x\to a}f(x) exists and equals 22 d) lim⁡x→af(x)\displaystyle \lim_{x\to a}f(x) exists and equals 55

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