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★ 8/10calculus Monotonicity inequality Casework

Problem

Let

f(x) = \ln(1+x) - \frac{ax}{1-x},

where $a$ is real.

1. When $a = 1$ , find the intervals of monotonicity of $f(x)$ . 2. If $f(x) \leqslant 0$ for all $-1 < x < 1$ , find the range of possible values of $a$ .

Answer

Solution

Difficulty	8/10
Topics	calculus, Monotonicity, inequality, Casework

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