The function D defined by D(x)=\left\{\begin{array}{ll} 0 & \text { if } x \text { is rational } \\ 1 & \text { if } x \text { is not

rational } \end{array}\right. is shown in the second video of Week 2 to have the property that lim x→b D(x) does not exist for any real number b. 1. Prove that lim x→∞ D(x) also does not exist. 2. Using the function D as a starting point, find a function E such that lim x→b E(x) does not exist any real number b but lim x→∞ E(x) does exist.

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