## Precalculus (10th Edition)

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General formula for average rate of change from $a$ to $b$: $\frac{f(b)-f(a)}{b-a}.$ Factor each polynomial: $$\lim_{x\to -1}\frac{f(x)-f(-1)}{x-(-1)}\\=\lim_{x\to -1}\frac{x^2+2x-((-1)^2+2(-1))}{x+1}\\=\lim_{x\to -1}\frac{x^2+2x+1}{x+1}\\=\lim_{x\to -1}\frac{(x+1)(x+1)}{(x+1)}.$$ Cancel the common factors: $$\lim_{x\to -1}(x+1)\\=(-1)+1=0$$