let F(t)= ∫_0 ^(+∞) ((sinx)/(x(1+x^2 ))) e^(−tx(1+x^2 )) dx witht≥0
1) caculate (dF/dt)(t)
2) find a simple form of F(t)
3) find the value of ∫_0 ^∞ ((sinx)/(x(1+x^2 )dx )).
let f(x)= arctan(2x)
1) calculate f^((n)) (x) then f^((n)) (0)
2) developp f at integr serie
3) let F(t)= ∫_0 ^t arctan(2x)dx
developp F at integr serie
4) give F(1) at form of serie.
Each of two long straight wires 4cm
apart carry equal electric currents
and experience a force of 2×10^(−4) N/m.
What is the magnitude of the
electric current in each?