Multivariable Calculus - Final Exam

Occur: when derivative is zero or undefined

Types: minimum, maximum, and saddle points

When do critical points occur and what are the three types of critical points?

ln(u)

Implicit differentiation: If F(x, y, z) is used to implicitly defined z as a function of x and y, then the chain rule says:

Work

If r(u, v) is a smooth parameterization of S with domain R, we have that the flux of F through S =

Relate the Fundamental Theorem of Line Integrals to the equation of work over a path C

Given a question such as this, what should you do after writing the bounds of z? (i.e., when trying to get the bounds of r)

Write down the formulas to convert coordinates from Cartesian to Spherical

What is the equation for a cone, with k being a constant?

What does the Extreme Value Theorem state?

What is the equation for a sphere centered at the origin with a radius r?