{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

1120_7

# 1120_7 - Week 7 Outline The Slope of a Parametric Curve Arc...

This preview shows pages 1–2. Sign up to view the full content.

Week 7 Outline The Slope of a Parametric Curve Arc Lengths for Parametric Curves Surface Areas for Parametric Curves Areas Bounded by Parametric Curves The Slope of a Parametric Curve Let C be the parametric curve x = f ( t ), y = g ( t ), where f 0 ( t ) and g 0 ( t ) are continuous on an interval I . If f 0 ( t ) 6 = 0 on I , then d y d x = g 0 ( t ) f 0 ( t ) . Remark We can rewrite the above equation in an easily remembered form: d y d x = d y d t d x d t , if d x d t 6 = 0 It can be seen from this equation that the curve has a horizontal tangent when d y d t = 0 (provided d x d t 6 = 0) and it has a vertical tangent when d x d t = 0 (provided d y d t 6 = 0). This information is useful for sketching parametric curves. It is also useful to consider d 2 y d x 2 , which can be found by d 2 y d x 2 = d d x d y d x = d d t ( d y d x ) d x d t . Examples 1. A curve C is defined by the parametric equations x = t 2 , y = t 3 - 3 t . (a) Show that C has two tangents at the point (3 , 0) and find their equations. (b) Find the points on C where the tangent is horizontal or vertical. (c) Determine where the curve is concave upward or downward. (d) Sketch the curve. 2. Find the coordinates of the points at which the given parametric curve has (i) a horizontal tangent and (ii) a vertical tangent.

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

### What students are saying

• As a current student on this bumpy collegiate pathway, I stumbled upon Course Hero, where I can find study resources for nearly all my courses, get online help from tutors 24/7, and even share my old projects, papers, and lecture notes with other students.

Kiran Temple University Fox School of Business ‘17, Course Hero Intern

• I cannot even describe how much Course Hero helped me this summer. It’s truly become something I can always rely on and help me. In the end, I was not only able to survive summer classes, but I was able to thrive thanks to Course Hero.

Dana University of Pennsylvania ‘17, Course Hero Intern

• The ability to access any university’s resources through Course Hero proved invaluable in my case. I was behind on Tulane coursework and actually used UCLA’s materials to help me move forward and get everything together on time.

Jill Tulane University ‘16, Course Hero Intern