((★BeMath⊚)/⊓)
(1) ∫ x tan^(−1) (x) dx ?
(2) Find the distance of the point
(3,3,1) from the plane Π with equation
(r^→ −i^→ −j^→ )•(i^→ −j^→ +k^→ ) = 0 , also
find the point on the plane that is
nearest to (3,3,1).
((♥JS♥)/(°js°))
Given a matrix A= ((( 3 2)),((−5 −4)) )
and A^2 +♭A−2I=0 where ♭ is a
constant , I= (((1 0)),((0 1)) ). If B =
(((−3♭ 2)),(( 5♭ −1)) ) , then A^(−1) B =
A particle in an electric and magnetic field is in motion.
The time equations are in polar coordinates.
r=r_0 e^(−(t/b)) and θ=(t/b) and b are positive constants.
1\Calculate the vector equation of the velocity of the particle.
2\Show that the angle (v_1 ^′ ,u_0 ′) is constant, and find the value.
3\Find the vector of acceleration of the particle.
4\Show that the angle (v_1 ^→ ,u_n ′) is constant, and find it.
5\Calculate the radius of this trajectory.