over the millennia the people who became the indo-europeans could have had a number of different homelands with their language evolving along the way.

How would the previous sentence be correctly capitalized?
Answer: Over the millennia the people who became the Indo-Europeans could have had a number of different homelands with their language evolving along the way.
they believed there was only only one particular equation for water waves and its solution was a sinusoidal function extending to infinity in both directions.

How would the previous sentence be correctly capitalized?
Answer: They believed there was only only one particular equation for water waves and its solution was a sinusoidal function extending to infinity in both directions.
check rates and availability for ciutadella park apartments. then proceed to booking.

How would the previous sentence be correctly capitalized?
Answer: Check rates and availability for Ciutadella Park Apartments. Then proceed to booking.
there is a very big difference between what a stuntman is doing and who will have the help of a stuntman some of the actors puts an honor in itself to perform their stunts and the other would prefer to avoid even the smallest of stunts.

How would the previous sentence be correctly capitalized?
Answer: There is a very big difference between what a stuntman is doing and who will have the help of a stuntman some of the actors puts an honor in itself to perform their stunts and the other would prefer to avoid even the smallest of stunts.