Parametric Equations and Vectors

In BC calculus the only application parametric equations and vectors is motion in a plane. Polar equations concern area and the meaning of derivatives. See the review notes for more detail and an outline of the topics. (only 3 items here) Motion Problems: Same Thing Different Context (11-16-2012) Implicit Differentiation of Parametric Equations (5-17-2014) A…

Type 8: Parametric and Vector Questions

The parametric/vector equation questions only concern motion in a plane. In the plane, the position of a moving object as a function of time, t, can be specified by a pair of parametric equations  or the equivalent vector . The path is the curve traced by the parametric equations or the tips of the position vector. . The velocity of the movement…

Parametric and Vector Equations

In the plane, the position of a moving object as a function of time, t, can be specified by a pair of parametric equations  or the equivalent vector . The path is the curve traced by the parametric equations or the tips of the position vector. . The velocity of the movement in the x- and y-direction is given by the vector . The vector…

Implicit Differentiation and Inverses

Implicit differentiation of relations is done using the Chain Rule.  Implicit Differentiation (from last Friday’s post. I discovered I never did a post on this topic before!) Implicit differentiation of parametric equations A Vector’s Derivative The inverse series  This series of posts reviews and expands what students know from pre-calculus about inverses. This leads to…

Good Question 9

This is a good question that leads to other good questions, both mathematical and philosophical. A few days ago this question was posted on a private Facebook page for AP Calculus Readers. The problem and illustration were photographed from an un-cited textbook. Player 1 runs to first base [from home plate] at a speed of…