Let f(x)=(tanx)/x and Lim x→0 ([f(x)]+x^2)^1/{f(x)} = e^lamda. Then find the value of lamda ?Where [.] Is G.I.F and {.} Is Fractional part

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.