Consider a simple, smooth (so that it has a well-defined tangent vector at every point), closed planar curve of total length L. Prove that the total integral of curvature with respect to arclength...
Consider a simple, smooth (so that it has a well-defined tangent vector at every point), closed planar curve of total length L. Prove that the total integral of curvature with respect to arclength...
The boundary of a thin plate is an ellipse with semiaxes a and b. Let L denote a line in the plane of the plate passing through the center of the ellipse and making an angle k with the axis...
Convert the integral ∫(-1 < x < 1) ∫(0 < y< sqrt(1-x2) ∫(( -sqrt(1-x2-y2) < z < 0) z2(x2+y2+z2)^(1/2) dzdydx into...
A circle is inside a square. The radius of the circle is decreasing at a rate of 3 meters per minute and the sides of the square are increasing at a rate of 4 meters per minute. When...
Find the domain, the range, and describe the level curves for the function f(x,y) = 1 - e^(-4x2 -9y2) I figure out that the domain is all real numbers The...
An inverted pyramid is being filled with water at a constant rate of 70 cubic centimeters per second. The pyramid, at the top, has the shape of a square with sides of length 3 cm, and the height is...
A police car is located 30 feet to the side of a straight road. A red car is driving along the road in the direction of the police car and is 210 feet up the road from the location of the...
Determining whether the Function is harmonic ? f(x,y) = 1/(x2+y2) - What I learned from class was that if fxx + fyy = 0 then the function is...
r(t)=< e5t cos(12t), e5tsin(12t), e5t > 1. Show that (5cos12t - 12sin12t)2 + (5sin12t + 12cos12t)2 = 132 2. Find the equation of the surface the curve...
r(t) = < e5tcos(12t), e5tsin(12t), e5t > 1. Find the unit binomial vector B(t) 2. Find the curvature k(t) 3. Find the torsion 4...
I am not really sure how to solve this problem... Evaluate the Limit: Limit (x,y,z) ----> (0,0,0) (x2+y2...
r(t) = < e5tcos(12t), e5tsin(12t), e5t > 1. Verify directly that a(t) (dot) B=0 2. What happens as t-> infinity and t-> -infinity for the curvature and...
Consider the transformation x=vcos(2piu), y=vsin(2piu) a)Describe the image S under T of the unit square R={(u,v,)|0<u<1,0<v<1} b)Find the area of S
When finding delta, use the absolute value of x-2 is less than 2 so that delta=min{2,__} This is what I've done so far: f(x)=1/x L=1/2 a=2 Find...
Find the volume enclosed by the surface (x^2+y^2+z^2)^2 = 2z(x^2+y^2). step by step solution would be much appreciated! :)
Please show work so that I can follow along
How can i get this?
it's a very long question so i took a screenshot of it here http://s4.postimg.org/qyasoc7p9/image.jpg i checked the marks scheme and i don't understand how do...
prove that three collinear points can determine a plane.
∫(x+3)/(4-x)5