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Let G(x) be defined for values of x such that 0 < x < 1 by G(x) = 1/n if the first non-zero digit in the decimal expansion of x

is the nth digit. 1. Why is G(x) defined if 0 < x < 1? 2. Why is G(0) not defined. \text { 4. Using the preceding, prove that } \lim _{x \rightarrow 0^{+}} G(x)=0 \text { . } \text { 3. Show that if } n \in \mathbb{N} \text { (and, hence, } n>0), 1 / n<\epsilon \text { and } \delta=10^{-n} \text { then }|G(x)|<\epsilon \text { for any } x \text { such } \text { that } 0

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