Question: The external display's max. resolution is 2560 x 1440, but the maximum resolution I can select on the display settings is 2048 x 1152.

What can I do to use the display in its max. resolution?

System: elementary OS 0.4.1 Loki

Display driver: Intel Corporation 3rd Gen Core processor Graphics Controller (rev 09)

Answer: 
Based on [answer](https://unix.stackexchange.com/questions/47749/cannot-add-new-mode-in-xrandr-for-external-monitor/)
 you can use `gtf height width refresh_rate` and get an new modeline as response and then you can create new mode with the output of the first command `xrandr --newmode modeline`, after that you need to ensure in which output you want to set up the modeline, you can check this with `xrandr -q` after get the response add the newmode to the desired output `xrandr --addmode OUTPUT "MODELINE"` and apply the new modeline `xrandr --output OUTPUT --mode MODELINE`.
Please open terminal pressing `Ctrl`+`Alt`+`T` and execute `xrandr -q` to see the connected displays and their current resolution.  

Then execute `xrandr --output <monitor_name> --mode <resolution>` to change resolution. For example, `xrandr --output eDP-2-1 --mode 2560x1440`