Search results
16 lis 2022 · In this section we will discuss how to find the arc length of a parametric curve using only the parametric equations (rather than eliminating the parameter and using standard Calculus techniques on the resulting algebraic equation).
- Assignment Problems
Section 9.4 : Arc Length with Parametric Equations. For all...
- Practice Problems
Section 9.4 : Arc Length with Parametric Equations. For all...
- Area With Parametric Equations
In this section we will discuss how to find the area between...
- Tangents With Parametric Equations
9.3 Area with Parametric Equations; 9.4 Arc Length with...
- Parametric Equations and Polar Coordinates
Chapter 9 : Parametric Equations and Polar Coordinates. In...
- 10.11 Root Test
In this section we will discuss using the Root Test to...
- Assignment Problems
20 sie 2024 · Learning Objectives. Determine derivatives and equations of tangents for parametric curves. Find the area under a parametric curve. Use the equation for arc length of a parametric curve. Apply the formula for surface area to a volume generated by a parametric curve.
Arc length is the distance between two points along a section of a curve. Determining the length of an irregular arc segment by approximating the arc segment as connected (straight) line segments is also called curve rectification. For a rectifiable curve these approximations don't get arbitrarily large (so the curve has a finite length).
16 lis 2022 · Now that we’ve derived the arc length formula let’s work some examples. Example 1 Determine the length of \ (y = \ln \left ( {\sec x} \right)\) between \ (0 \le x \le \frac {\pi } {4}\). Example 2 Determine the length of \ (x = \frac {2} {3} {\left ( {y - 1} \right)^ {\frac {3} {2}}}\) between \ (1 \le y \le 4\).
The arc length formula can be used to derive the formula for the circumference of a circle. A circle of radius r, centered at the origin, may be parametrized by
7.2.1 Determine derivatives and equations of tangents for parametric curves. 7.2.2 Find the area under a parametric curve. 7.2.3 Use the equation for arc length of a parametric curve. 7.2.4 Apply the formula for surface area to a volume generated by a parametric curve.
5 lip 2023 · In this section we will introduce parametric equations and parametric curves (i.e. graphs of parametric equations). We will graph several sets of parametric equations and discuss how to eliminate the parameter to get an algebraic equation which will often help with the graphing process.
