If lim _x→a f(x) = lim _x→a [f(x)] (where[.] denotes the greatest integral function) and f(x) is non constant continous function, then show that lim x→a f(x) is integer

the diameter of a roller is 84 cm and its length is 120 cm. it takes 500 complete revolution to  move once over to level a playground. find the area of the playground in square m?

Find dy/DX when y=x^sinx+sin-1√x.

 

Please give me the solution of this problem. 

Solve the differential equation y’’+2ty’-4y=1, y(0)=y’(0)=0.