Suppose a certain function in continuous at [itex]c[/itex] and [itex](c. f(c))[/itex] exists, then which of the two could be false: [itex]\displaystyle \lim_{x \rightarrow c^-} {f(x)} = \lim_{x \rightarrow c^+} {f(x)}[/itex], and [itex]\displaystyle f'(c)[/itex]?(adsbygoogle = window.adsbygoogle || []).push({});

I feel like both could be false, because if the formal derivative at a point exists, then the left and right hand limits much be equal -- but the function could be [itex]f(x) = |x|[/itex], which means that [itex]\displaystyle \lim_{x \rightarrow 0^-} {f(x)} \neq \lim_{x \rightarrow 0^+} {f(x)}[/itex] (but [itex]\displaystyle \lim_{x \rightarrow 0} {f(x)} = 0[/itex]) and [itex]f'(0) = \frac {d}{dx}|0|[/itex] does not exist. I feel like I'm missing something, cause the nuances around continuity and differentiability have always been confusing (and vague) to me.

Thank-you

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# B Continuous but Not Differentiable

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