Prove that each of the following inequalities holds.
a) 2x + 0.7 < ex for all x ≥ 1.
b) log x <√x − 0.6 for all x ≥ 4.
c) sin2 x ≤ 2|x| for all x ∈ R.
d) 1 − sin x ≤ ex for all x ≥ 0.
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