Question: Determine a condition on |x - 1| that will assure that: (a) |x2 - 1| < 1/2, (b) |x2 - 1 < 1/10-3, (c) |x2

Determine a condition on |x - 1| that will assure that:
(a) |x2 - 1| < 1/2,
(b) |x2 - 1 < 1/10-3,
(c) |x2 - 1| < 1/n for a given n ∈ N,
(d) |x3 - 1| < 1/n for a given n ∈ N.

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