2. Prove that each of the following inequalities. (a) VI + 2x < 1 + x for...

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2. Prove that each of the following inequalities.

(a) VI + 2x < 1 + x for all x> O.

(b) log x ::; x-I for all x ::::: 1.

(c) 7(x-l)

(d) sin2 x::; 21xl for all x E R.

~. This exercise is used in Sections 7.4 and 12.5. Assume that eX is differentiable on R with (ex)' = eX.

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