An Exp-Log Domination

Problem

The inequality

a(x21)1xlnx+e1x>0a\left(x^2 - 1\right) - \frac{1}{x} - \ln x + e^{1-x} > 0

holds for all x>1x > 1. Find the range of possible values of aa.

Answer

Solution

Difficulty8/10
Topicscalculus, Convexity, Monotonicity, inequality

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