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A curve has the equation $f(x)=\sin x$. Which of the following is equal to $f'(\pi)$?

A

$\lim \limits_{x \to 0} \cfrac{\sin (x)}{x}$

B

$\lim \limits_{h \to 0} \cfrac{\sin (\pi+h)}{h}$

C

$\lim \limits_{x \to \pi} \cfrac{\sin (x+h)-\sin (x)}{h}$

D

$\lim \limits_{h \to 0} \cfrac{\sin (\pi+h)-1}{h}$

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