Vectors Lesson
1 hr 15 min 9 Examples
- Overview of vector operations and components
- Limits of vector functions (Examples #1-3)
- Derivatives of vector functions (Examples #4-6)
- Integrals of vector functions (Examples #7-8)
- Given a(t) and initial conditions, find the velocity and position functions (Example #9)
Parametric Lesson
1 hr 50 min 11 Examples
- Overview of plane curves defined parametrically
- Notation for parametric functions and how to eliminate the parameter
- Slope of parametric curves: first and second derivative formulas
- Find the first and second derivative of the parametric function (Examples #1-2)
- Find dy/dx and d²y/dx² for the parametric curve (Examples #3-4)
- Horizontal and vertical tangents for parametric curves
- Find the points where the tangent is horizontal or vertical (Examples #5-6)
- How to find speed and arc length for parametric curves
- Set up an integral for the length of the parametrically defined curve (Examples #7-8)
- Find the distance traveled along the parametric curve over the interval (Example #9)
- Finding area of parametric functions
- Find the area bounded by the parametric curve (Example #10)
- Calculate the area bounded by the parametric function (Example #11)
Parametric Vector Applications
1 hr 22 min 5 Examples
- Given the velocity vector and initial position, find the acceleration vector (Example #1a)
- Find the position vector of the particle (Example #1b)
- For what time does the line tangent to the path of the particle have the given slope? (Example #1c)
- Find the slope of the line the particle approaches as t approaches infinity (Example #1d)
- Given the velocity and initial position, write the equation of the line tangent (Example #2a)
- Find the speed of the object (Example #2b)
- Find the distance traveled by the object over the interval (Example #2c)
- Write the integral expression to find the position (Example #2d)
- Velocity and initial position in parametric form: find velocity, speed, and acceleration at a given time (Example #3a)
- Write the equation of the line tangent to the path (Example #3b)
- Write the integral expression for the distance traveled by the particle (Example #3c)
- Given velocity and initial position in parametric form, at what point is the object at a vertical tangent? (Example #4a)
- Evaluate the limit at infinity for the slope of the line tangent to the curve (Example #4b)
- Write an improper integral expression to represent the horizontal asymptote (Example #4c)
- Object moving along a parametrically defined curve: for which values is the curve concave upward? (Example #5a)
- Find the area bounded by the parametric curve and the x-axis (Example #5b)
Chapter Test
1 hr 14 min 22 Examples
- 22 Challenging Practice Problems
- Great for checking your knowledge
- Perfect for preparing for an in-class assessment