A scalar function f : which is never zero has the properties
and
Evaluate the integral
where
is the surface of the unit sphere
and means the directional derivative of f in the direction of the outward pointing unit normal on .
A scalar function f : which is never zero has the properties and Evaluate the integral...
Use the transformation and to evaluate the integral where is the region bounded on the by the ellipse Let S be the image of R under T on the . Sketch regions R and S. Set up the integral as an iterated integral of a function over region S. Use technology to evaluate the integral. Give the exact answer. We were unable to transcribe this imageWe were unable to transcribe this imageR xdA We were unable to transcribe this imageWe were...
Evaluate the line integral, where C is the given curve. where C is the curve of intersection of the sphere and the plane oriented counterclockwise when viewed from the positive x-axis. We were unable to transcribe this image-- + +22=1 r - y=0
Solve the Following The Scalar field gives the temperature at a given point. a.) The temperature at (2,12,-3) is only 5 degrees Celsius. In what direction should you move to experience the greatest possible increase in temperature, and what is the rate of change. b.) At (2,12,-3), what is the rate of change (directional derivative) if it goes in the direction We were unable to transcribe this imageWe were unable to transcribe this image
2. Evaluate the surface integral (cos(zz),3ev,-e y) and S is the part of the sphere z2+-2)2 8 where F(x, y,z) that lies above the ry-plane, oriented by outward normal. 2. Evaluate the surface integral (cos(zz),3ev,-e y) and S is the part of the sphere z2+-2)2 8 where F(x, y,z) that lies above the ry-plane, oriented by outward normal.
A) Evaluate the surface integral Where , , B) Find the equation of the plane tangent to the surface at the point on the surface. Express the plane in standard form We were unable to transcribe this imageSir(u, v) = 5cosui + 5sinuj + uk VI VI Ο Κυ r(u, v) = ui + 3vj + u’uk (2.9.12) (ar + by + cz = d)
For any vector field F⃗ and any scalar function f we define a new field a) Assuming that the appropriate partial derivatives are continuous, show the following formula: b) Let ⃗x = x⃗i + y ⃗j + z ⃗k and the vector field Use the formula found in a) to answer the following question: is there a number p such that F⃗ is incompressible (that is, its divergence is zero)? f F)(x,y,z) = f(x,y,z)F(x,y, z) We were unable to transcribe...
2. Given the vector field F-ki/r+zk22, evaluate the scalar surface integral (1) over the surface of a closed cylinder about the z-axis specified by 2 = +3 and r = 2, as described in Fig. 1, where ki and ky are constants. Fig. 1. A cylindrical surface.
Let a. Find at (2,1) b. Find the directional derivative of f at (2,1) in the direction of -i+3j f(:,y) = xy - 1 We were unable to transcribe this image
Let ⊂ be a rectangle and let f be a function which is integrable on R. Prove that the graph of f, G(f) := {(x, f(x)) ∈ : x ∈ }, is a Jordan region and that it has volume 0 (as a subset of ). We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image
Evaluate the flux F across the positively oriented surface S where and S is the boundary of We were unable to transcribe this imageWe were unable to transcribe this imageWe were unable to transcribe this image