Question: Let x R. a) Prove that |x| < 2 implies |x2 - 4| < 4|x - 2|. b) Prove that |x| < 1 implies

Let x ∈ R.
a) Prove that |x| < 2 implies |x2 - 4| < 4|x - 2|.
b) Prove that |x| < 1 implies |x2 + 2x - 3| < 4|x - 1|.
c) Prove that -3 < x < 2 implies |x2 + x - 6| < 6|x - 2|.
d) Prove that -1 < x < 0 implies |x3 - 2x + 1| < 1 .25|x - 1|.

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