Question: f(x) = 2x – tan<sup>–1</sup>x – log (x + $\sqrt{1 + x^{2}}$) is monotonic increasing when –...

Question

f(x) = 2x – tan^–1x – log (x + $\sqrt{1 + x^{2}}$ ) is monotonic increasing when –

Answer 1

f '(x) = 2– $\frac{1}{1 + x^{2}}$ – $\frac { 1 } { \left( x + \sqrt { 1 + x ^ { 2 } } \right. }$ $\left( 1 + \frac{2x}{2\sqrt{1 + x^{2}}} \right)$

Ž f '(x) = 2 – $\frac{1}{1 + x^{2}} - \frac{1}{\sqrt{1 + x^{2}}}$

Ž f ' (x) = $\frac{2(1 + x^{2}) - 1 - \sqrt{1 + x^{2}}}{(1 + x^{2})}$ > 0

Ž 2x² + 1 > $\sqrt{1 + x^{2}}$

Which is true " x Ī R

Question: f(x) = 2x – tan<sup>–1</sup>x – log (x + \(\sqrt{1 + x^{2}}\)) is monotonic increasing when –...