Mathematics - Limits Question with Solution | TestHub

$$\underset{x\to \infty }{\lim }x-{\log }_e\left(\frac{e^x+e^{-x}}{2}\right)$$

$$\begin{array}{rl}& \underset{x\to \infty }{\lim }x-{\log }_e{e}^x\left(\frac{1+e^{-2x}}{2}\right)\\ & \underset{x\to \infty }{\lim }x-x-{\log }_e\left(\frac{1+e^{-2x}}{2}\right)\\ & \underset{x\to \infty }{\lim }-{\log }_e\left(\frac{1}{2}\right)={\log }_{e}2\end{array}$$