patented 3-position reclining headrest

How would the previous sentence be correctly capitalized?
Answer: Patented 3-position reclining headrest
relying on a larger number of diffuse power sources can increase a power system's resilience against blackouts.

How would the previous sentence be correctly capitalized?
Answer: Relying on a larger number of diffuse power sources can increase a power system's resilience against blackouts.
there were other students at konigsberg at this time who would become important in the development of mathematics, in particular wangerin studied for his doctorate around the same time as weber worked for his habilitation.

How would the previous sentence be correctly capitalized?
Answer: There were other students at Konigsberg at this time who would become important in the development of mathematics, in particular Wangerin studied for his doctorate around the same time as Weber worked for his habilitation.
press circle out from the center and radius .

How would the previous sentence be correctly capitalized?
Answer: Press circle out from the center and radius .