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4. Please work each part. (a) Discuss the existence or non-existence of limx→0 2 sin 1...

4. Please work each part. (a) Discuss the existence or non-existence of limx→0 2 sin 1 x − x 2 cos 1 x using the limit theorems. (b) Let I be an open interval with a ∈ I and suppose that f is a function defined on I\{a}. Suppose that limx→a (f(x) + D(x)) exists, where D(x) = χQ(x) is the Dirichlet function. Show that limx→a f(x) does not exist.

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