Given v′(t)=2ti+j, find the arc length of the curve v(t) on the
interval [−2,3]. You may use technology to approximate your
solution to three decimal places.
(1 point) If C is the curve given by
r(t)=(1+5sint)i+(1+3sin2t)j+(1+3sin3t)k, 0≤t≤π2 and F is the radial
vector field F(x,y,z)=xi+yj+zk, compute the work done by F on a
particle moving along C.
Problem 2 Find max, min, point of infliction for
a. f(t)=c (e^(-bt)-e^at ) for t≥0 where a>b>0, c>0
b. f(x)=2x^3+3x^2-12x-7 for -3≤x≤2
c. f(x)=(x+3)/(x^2+7) for -∞≤x≤+∞
(a) Find the exact length of the curve y = 1/6 (x2 +
4)(3/2) , 0 ≤ x ≤ 3. (b) Find the exact area of the
surface obtained by rotating the curve in part (a) about the
y-axis.
I got part a I NEED HELP on part b
FOR THE PARAMETRIZED PATH r(t)=
e^tcos(πt)i+e^tsin(πt)j+e^tk
a) find the velocity vector, the unit
tangent vector and the arc lenght between t=0 and t=1
b) find a point where the path given by r(t)
intersects the plane x-y=0 and determine the angle of intersection
between the tangent vector to the curve and the normal vector to
the plane.