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Answer:
B. -1
Explanation:
A graph can show you that the expression approaches -1 as x approaches 2π.
The limit is -1.
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The expression evaluated at x=2π is 0/0, an indeterminate form. This suggests that L'Hopital's rule is applicable. Applying that, we have ...
lim = (f'(2π) -f'(x))/(x-2π)' = -cos(x)/1
Evaluated at x=2π, this is ...
lim = -1