User:Melikamp/ma225

README
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Polar Coordinates
Sketch the following polar curves without using a computer.

Sketch the following sets of points.

Calculus in Polar Coordinates
Find points where the following curves have vertical or horizontal tangents.

Sketch the region and find its area.

Cross Product
Find $$\mathbf u\times\mathbf v$$ and $$\mathbf v\times\mathbf u$$

Find the area of the parallelogram with sides $$\mathbf u$$ and $$\mathbf v$$.

Prove the following identities or show them false by giving a counterexample.

Length of Curves
Find the length of the following curves.

Limits And Continuity
Evaluate the following limits.

At what points is the function f continuous?

Use the two-path test to show that the following limits do not exist. (A path does not have to be a straight line.)

Partial Derivatives
Find the four second partial derivatives of the following functions.

Chain Rule
Find $$df/dt.$$

Find $$f_s,\ f_t.$$

Tangent Planes
Find an equation of a plane tangent to the given surface at the given point(s).

Maximum And Minimum Problems
Find critical points of the function f. When possible, determine whether each critical point corresponds to a local maximum, a local minimum, or a saddle point.

Find absolute maximum and minimum values of the function f on the set R.

Double Integrals over Rectangular Regions
Evaluate the given integral over the region R.

Evaluate the given iterated integrals.

Double Integrals over General Regions
Evaluate the following integrals.

Use double integrals to compute the volume of the given region.

Triple Integrals
In the following exercises, sketching the region of integration may be helpful.

Vector Fields
One can sketch two-dimensional vector fields by plotting vector values, flow curves, and/or equipotential curves.

Conservative Vector Fields
Determine if the following vector fields are conservative on $$\mathbb R^2.$$

Determine if the following vector fields are conservative on their respective domains in $$\mathbb R^3.$$ When possible, find the potential function.

Divergence Theorem
Compute the net outward flux of the given field across the given surface.