Study guide: you need to know everything.

However, here are some  Highlights:

Chapters 18, 19:
You need to be able to recognize and plot cylinders, simple quadrics.
You need to know the formulas for changing coordinates to cylindrical or spherical and use them
for integration or substitutions in partial differential equations. You need to know dV in these coordinates.
You need to know the equation of the tangent plane; that grad f points in the direction of the fastest increase,
the formula for a normal vector to a surface given as a graph z=f(x,y) or as an equation F(x,y,z)=0.
You need to be able to use the chain rule.  Use it in substitutions in differential equations.
Implicit functions.
Extrema: local, absolute, with constraints (Lagrange multipliers).

The second derivative test  is included on the formula sheet.
Use of Taylor polynomials (the formula will be provided).

Chapter 20: everything!
(Except: the formulas I-IV of 20.3 will be provided if needed; no questions will be asked regarding the gravitational force.)

Chapter 21:

Line integrals:
calculation, interpretation as work or flow, or flux.
Independence on path for F=Li+Mj: the diagram on top of page 762 completed with: implies dM/dx=dL/dy
and we have equivalence if L, M, are continuously differentiable on the domain under discussion.