MathDB

Define the function

f(x)

as : \displaystyle f(x)\equal{}\left\{ \begin{array}{ll} \frac{\ln (1\plus{}x)}{1\plus{}x}\ (x\geq 0) & \\ \frac{\ln (1\minus{}x)}{1\minus{}x}\ (\minus{}1\leq x<0) & \end{array} \right. 1. Examine the variation of

f(x)

and find the maximum and minimum value of

f(x)

. 2. Find the value of

a

for which \int_{\minus{}1}^{e\minus{}1} |f(x)\minus{}a|\ dx is minimized for

0\leq a\leq \frac{1}{e}

Problem Statement