Cho hàm số

C

- Hướng dẫn giải

Đáp án C

Ta có: $f\text{'}\left(x\right)=2018.\frac{\left(e^{\frac{x}{2018}+\sqrt{e}}\right)\text{'}}{e^{\frac{x}{2018}}+\sqrt{e}}=\frac{e^{\frac{x}{2018}}}{e^{\frac{x}{2018}}+\sqrt{e}}=g\left(x\right)$ 

Lại có: $g\left(a\right)+g\left(2018-a\right)=\frac{e^{\frac{a}{2018}}}{e^{\frac{a}{2018}}+\sqrt{e}}+\frac{e^{1-\frac{a}{2018}}}{e^{1-\frac{a}{2018}}+\sqrt{e}}=\frac{e^{\frac{a}{2018}}}{e^{\frac{a}{2018}}+\sqrt{e}}+\frac{\sqrt{e}}{e^{\frac{a}{2018}}+\sqrt{e}}=1$ 

Do đó $T=g\left(1\right)+g\left(2017\right)+g\left(2\right)+g\left(2016\right)+\mathrm{...}+g\left(1010\right)+g\left(1009\right)=1008+g\left(1009\right)$ 

$=1008+\frac{1}{2}=\frac{2017}{2}.$