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- A soda can has a volume of 25 cubic inches. Let x denote its radius and h its height, both in inches. a. Using the fact that the volume of the can is 25 cubic inches, express h in terms of x. b. Express the total surface area S of the can in terms of x.Show that f(x,y)=exyx is differentiable at point (1,0) using the definition of differentiability.How would I go about solving ∭xzdV, where E is bounded by the planes z = 0, z=y, and the cylinder x2 + y2 = 1 in the half-space y ≥ 0 ? Thanks for you help. :)
- How would I solve ∭xzdV, where E is bounded by the planes z = 0, z=y, and the cylinder x2 + y2 = 1 in the half-space y ≥ 0 ? Thanks for you help in advance. :)Calculate ∫c Pdx + Qdy + Rdz, where:F = (P,Q,R) = (y,z,x) and C is the intersection of x + y =2 and x2 + y2 + z2 = 2x + 2y traversed counterclockwise when viewed from the originif there is to calculate limits to use in the integral, let it clear how toIf I let F=M(x,y)i + N(x,y)j be continously differentiable on R^2. How do I prove that curlF = dN/dx - dM/dy?
- (a) Express the mass M of a thin wire in 3-space as a line integral. (b) Express the length of a curve as a line integralAssume that ƒ is differentiable on a<=x<=b and that ƒ(b)<ƒ(a). Show that ƒ′ is negative at some point between a and b.Suppose that a thin metal plate of area A and constant density doccupies a region R in the xy-plane, and let My be the plate’s momentabout the y-axis. Show that the plate’s moment about the linex = b is My - bδA if the plate lies to the right of the line, and
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