evaluate
C
(y + 4 sin x)
dx + (z2 + 8 cos
y) dy +
x3dz
where C is the curve
r(t) =
sin t, cos t, sin
2t
, 0 ≤ t ≤ 2π.
(Hint: Observe that C lies on the surface
z = 2xy.)
For
the differential equation (2 -x^4)y" + (2*x -4)y' + (2*x^2)y=0.
Compute the recursion formula for the coefficients of the power
series solution centered at x(0)=0 and use it to compute the first
three nonzero terms of the solution with y(0)= 12 , y'(0) =0
1. Find absolute max and min of f(x,y)=
x^2- xy + y^2 +1 on the closed triangular plate in the first
quadrant x=0, y=4, y=x
2. Given position of a particle by π (t)= Cos2ti + 3
sin2ti, Find the
particle velocity and acceleration at t=0