Two Sharp Lower Bounds

★ 7/10Extrema calculus Substitution Estimation inequality

Problem

Let $f(x) = \mathrm{e}^x - \ln(x + a)$ .

1. If $a = 2$ , prove that $f(x) > \dfrac{1}{6}$ . 2. If $a = \dfrac{9}{4}$ , prove that $f(x) > 0$ .

Answer

Solution

Difficulty	7/10
Topics	Extrema, calculus, Substitution, Estimation, inequality

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