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Determine the square of the arc element for the curvilinear coordinate system

(u,v,w) whose coordinates are related to the Cartesian coordinates as follows:

x = 3u + v − w; y = u + 2v + 2w;z = 2u − v − w.

(u,v,w) whose coordinates are related to the Cartesian coordinates as follows:

x = 3u + v − w; y = u + 2v + 2w;z = 2u − v − w.

Coordinates whose curves are mutually perpendicular at each point are called …………

Cylindrical Coordinates

Spherical Coordinates

Orthogonal Curvilinear coordinates

Ellipsonic Cylindrical Coordinates

Cylindrical Coordinates

Spherical Coordinates

Orthogonal Curvilinear coordinates

Ellipsonic Cylindrical Coordinates

Given that

A=sinti+costj+tk

, find

∣∣∣d^2A/dt^2∣∣∣

7

3

2

1

A=sinti+costj+tk

, find

∣∣∣d^2A/dt^2∣∣∣

7

3

2

1

1)Find the point of maximum curvature on the graph of y=e^(x)

2)Find the minimum and maximum curvatures of the ellipse r(t)=(acost,bsint),0<=t<=2pi, where a>b

2)Find the minimum and maximum curvatures of the ellipse r(t)=(acost,bsint),0<=t<=2pi, where a>b

Find the slope of c(t)=(t/2,(t^(2)/4) -t) at t=2

find a vector parametrization v(t),t (0,3) of the path(or loop) ABCA where A(1,0,1),B(1,1,0),C(0,1,1)

Find the Bezier curve where the control points are P(2,3),P1(2,0),P2(3,1),P3(4,4)

A curve has the equation y = x/16 * (5-x)^4. Calculates the values of x for which dy/dx =0 . Given that a small change,p,is made in the x-coordinate at the point (4,0.25), calculate,in terms of p, the approximate change in the y-coordinate .

find the tangent line of the curve at the points t=+1,-1,0

r(s)=(s^2-1,s(s^2-1),0)

r(s)=(s^2-1,s(s^2-1),0)

let r(s)=(x(s),y(s),0) be a unit speed curve prove that K=|x'y''-x''y'|