Calculus/Multivariable and differential calculus:Exercises< Calculus
Sketch the following polar curves without using a computer.
Sketch the following sets of points.
Calculus in Polar CoordinatesEdit
Find points where the following curves have vertical or horizontal tangents.
Sketch the region and find its area.
Vectors and Dot ProductEdit
Find the area of the parallelogram with sides and .
Prove the following identities or show them false by giving a counterexample.
Calculus of Vector-Valued FunctionsEdit
Motion in SpaceEdit
Length of CurvesEdit
Find the length of the following curves.
Parametrization and Normal VectorsEdit
Equations of Lines And PlanesEdit
Limits And ContinuityEdit
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.)
Find the four second partial derivatives of the following functions.
Find an equation of a plane tangent to the given surface at the given point(s).
Maximum And Minimum ProblemsEdit
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 RegionsEdit
Evaluate the given integral over the region R.
Evaluate the given iterated integrals.
Double Integrals over General RegionsEdit
Evaluate the following integrals.
Use double integrals to compute the volume of the given region.
Double Integrals in Polar CoordinatesEdit
In the following exercises, sketching the region of integration may be helpful.
Cylindrical And Spherical CoordinatesEdit
Center of Mass and CentroidEdit
One can sketch two-dimensional vector fields by plotting vector values, flow curves, and/or equipotential curves.
Conservative Vector FieldsEdit
Determine if the following vector fields are conservative on
Determine if the following vector fields are conservative on their respective domains in When possible, find the potential function.
Divergence And CurlEdit
Compute the net outward flux of the given field across the given surface.