Questions from General Calculus

Q: Plot the vector field and guess where div F > 0 and

Plot the vector field and guess where div F > 0 and where div F

Q: Find a parametric representation for the surface. The part of

Find a parametric representation for the surface. The part of the ellipsoid x2 + 2y2 + 3z2 = 1 that lies to the left of the xz-plane

Q: (a). What is an initial-value problem for a

(a). What is an initial-value problem for a second-order differential equation? (b). What is a boundary-value problem for such an equation?

Q: Is the vector field shown in the figure conservative? Explain.

Is the vector field shown in the figure conservative? Explain.

Q: Use a graphing device to produce a graph that looks like the

Use a graphing device to produce a graph that looks like the given one.

Q: Use a graphing device to produce a graph that looks like the

Use a graphing device to produce a graph that looks like the given one.

Q: Use Exercise 29 to show that the line integral ∫C y

Use Exercise 29 to show that the line integral ∫C y dx + x dy + xyz dz is not independent of path. Exercise 29: Show that if the vector field F = P i + Q j + R k is conservative a...

Q: Evaluate the surface integral ∫∫S F ∙ dS for the

Evaluate the surface integral ∫∫S F ∙ dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientat...

Q: A solid occupies a region E with surface S and is immersed

A solid occupies a region E with surface S and is immersed in a liquid with constant density . We set up a coordinate system so that the xy-plane coincides with the surface of the liquid, and positive...

Q: Find an equation of the tangent plane to the given parametric surface

Find an equation of the tangent plane to the given parametric surface at the specified point.