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1.3 Limits

1.

(a) $12$ (b) $\displaystyle{\frac{1}{4}}$ (c) $-2$ (d) $-8$ (e) $1$ (f) $\displaystyle{\frac{2}{3}}$ (g) $4$

2.

(a) $\displaystyle{3}$ (b) $2$ (c) $1$ (d) 0

3.

$\vert\vert f(x)\vert - 0\vert = \vert f(x) - 0\vert$．For all $\varepsilon > 0$, there exists $\delta$ such that $\vert x - a\vert < \delta$ implies $\vert\vert f(x)\vert - 0\vert = \vert f(x) - 0\vert < \varepsilon$