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In the graph shown below, $f$ has a vertical tangent at $x=2$ and horizontal tangents at $x=-4$ and $x=8$.

Which of the following statements is NOT true?

A

$\lim \limits_{x \to -2^-} f(x)= \lim \limits_{x \to -2^+} f(x)$

B

$\lim \limits_{x \to 2} f(x)=f(2)$

C

$\lim \limits_{h \to 0} \cfrac{f(8+h)-f(8)}{h}=0$

D

$\lim \limits_{x \to -2^+} \cfrac{f(x)-f(-2)}{x+2} =\lim \limits_{x \to -2^-} \frac{f(x)-f(-2)}{x+2}$

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