Question

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Answer 1

Oh, crap. I forgot to add: f'(-1).

Answer 2

\[\frac{dy}{dx} = \lim_{h \rightarrow 0} \frac{ \frac{1}{x+h-2} - \frac{1}{x-2} }{h}\]

Answer 3

\[\frac{dy}{dx} = \lim_{h \rightarrow 0} \frac{ \frac{x-2- (x+h-2)} {(x-2)(x+h-2)}}{h}\]

Answer 4

\[\frac{dy}{dx}= \lim_ {h \rightarrow 0} \frac{ -\frac{h}{(x-2)(x+h-2)} }{h} = \lim_{h \rightarrow 0 } \frac{-1}{(x-2)(x+h-2)}\]

Answer 5

\[\frac{dy}{dx} = \frac{-1}{(x-2)(x-2)} = \frac{-1}{(x-2)^2}\]

Answer 6

\[f'(-1)= -\frac{1}{9}\]

Answer 7

I see! I really do appreciate you taking the time to solve this problem for me.