Please capitalize where necessary: and where a theorem may present some problem, he may always look down to the numerical examples for help.
A: And where a theorem may present some problem, he may always look down to the numerical examples for help.

Please capitalize where necessary: 1905: dimitri mendeleev was awarded the copley medal by the royal society of great |britain.
A: 1905: Dimitri Mendeleev was awarded the Copley Medal by the Royal Society of Great |Britain.

Please capitalize where necessary: vehicle hire company offering a wide range of vehicles including cars, vans, pick-ups, lutons and buses.
A: Vehicle hire company offering a wide range of vehicles including cars, vans, pick-ups, lutons and buses.

Please capitalize where necessary: united states and china lead climate negotiators todd stern (left) and xie zhenhua sparred in separate public appearances following the tianjin negotiations
A:
United States and China lead climate negotiators Todd Stern (left) and Xie Zhenhua sparred in separate public appearances following the Tianjin negotiations