If f(x) = sin x, then lim 2pi)-f(x) / x-2 pi equals? x->2pi (2pi)-f(x) / x-2 pi =

Question

If f(x) = sin x, then lim 2pi)-f(x) / x-2 pi equals?

x->2pi

(2pi)-f(x) / x-2 pi =

A) -2 pi

B) -1

C) 1

D) 2 p

Side Note- If confused it's asking what is the limit as x approaches 2pi of F(2pi) -f(x) over x - 2p

Answer 1

Recall that f'(c) = lim_x→c [(f(x) - f(c)) / (x - c)]

f(x) = sinx

So, the limit as x approaches 2π of [f(2π) - f(x)] / (x - 2π)

= -f'(2π) = -cos(2π) = -1