Questions from General Calculus

Q: (a). Write the definition of the triple integral of f

(a). Write the definition of the triple integral of f over a rectangular box B. (b). How do you evaluate ∫∫∫B f (x, y, z) dV? (c). How do you define ∫∫∫B f (x, y, z) dV if E is a bounded solid region...

Q: Define the linearization of f at (a, b). What

Define the linearization of f at (a, b). What is the corresponding linear approximation? What is the geometric interpretation of the linear approximation?

Q: The vector field F is shown in the xy-plane and

The vector field F is shown in the xy-plane and looks the same in all other horizontal planes. (In other words, F is independent of z and its z-component is 0.) (a). Is div F positive, negative, or...

Q: Solve the differential equation. 3 d2V/dt2 + 4

Solve the differential equation. 3 d2V/dt2 + 4 dV/dt + 3V = 0

Q: Use the Divergence Theorem to calculate the surface integral ∫∫S F

Use the Divergence Theorem to calculate the surface integral ∫∫S F  dS; that is, calculate the flux of F across S. F = |r |2 r, where r = x i + y j + z k, S is the sphere with radius R and center the...

Q: Use the Divergence Theorem to calculate the surface integral ∫∫S F

Use the Divergence Theorem to calculate the surface integral ∫∫S F  dS; that is, calculate the flux of F across S. F (x, y, z) = ey tan z i + y√3 - x2 j + x sin y k, S is the surface of the solid tha...

Q: Evaluate the surface integral. ∫∫S (x2z + y2z

Evaluate the surface integral. ∫∫S (x2z + y2z) dS, where S is the part of the plane z = 4 + x + y that lies inside the cylinder x2 + y2 = 4

Q: Use a computer algebra system to plot the vector field F (

Use a computer algebra system to plot the vector field F (x, y, z) = sin x cos2y i + sin3y cos4z j + sin5z cos6x k in the cube cut from the first octant by the planes x = π/2, y = π/2, and z = π/2. T...

Q: Solve the initial-value problem. y'' + 3 =

Solve the initial-value problem. y'' + 3 = 0, y (0) = 1, y' (0) = 3

Q: Solve the initial-value problem. y'' - 2y' -

Solve the initial-value problem. y'' - 2y' - 3y = 0, y (0) = 2, y'(0) = 2