BMCC MTH 253 - Analytic Geometry in Calculus (7 pages)

Previewing pages 1, 2 of 7 page document View the full content.
View Full Document

Analytic Geometry in Calculus



Previewing pages 1, 2 of actual document.

View the full content.
View Full Document
View Full Document

Analytic Geometry in Calculus

43 views

Lecture Notes


Pages:
7
School:
Blue Mountain Community College
Course:
Mth 253 - CALCULUS

Unformatted text preview:

MTH 253 Calculus Other Topics Chapter 11 Analytic Geometry in Calculus Section 11 2 Tangent Lines Arc Length for Parametric and Polar Curves Copyright 2006 by Ron Wallace all rights reserved Reminder Tangent Lines to a Cartesian Function at a Point y f x Find the point x0 f x0 Determine y f x f x0 x0 Evaluate f x0 m y f x0 f x0 x x0 Example x f t Slope at a Point of a Parametric Curve y g t Differentiate each equation giving dx f t dt dy g t dt Divide assuming dx dt 0 g t dy dt dy f t dx dt dx Therefore the slope can be determined without eliminating the parameter Slope at a Point of a Parametric Curve x f t y g t dy g t dx f t What is happening when dx dt i e f t is 0 Vertical tangent What is happening when dy dt i e g t is 0 Horizontal tangent What is happening when both are zero Singular Point Analyzed Case by Case Tangent Line to a Parametric Curve x f t Example Find the equation of the line tangent to the curve when t 2 y g t dy g t dx f t x 2sin t 2 y t 5 Pt 2sin t t 2 5 1 8 1 dy 2t m 4 8 dx 2 cos t y 1 4 8 x 1 8 4 8 x 7 64 When is the tangent line horizontal vertical Slope at a Point of a Polar Curve r f q From section 11 1 x r cos q y r sin q Essentially parametric equations parameter is so differentiating implicitly dr r cos q sin q dy dy dq dq dx dx dq r sin q dr cos q dq Tangent Lines to a Polar Curve Example Find the points where the tangent lines are horizontal or vertical dy 4 cos 2q cos q 8sin 2q sin q m dx 4 cos 2q sin q 8sin 2q cos q 2 4 cos q 6 cos q 5 2 4sin q 6sin q 5 horizontal tangents at 90 24 156 vertical tangents at 0 180 66 114 dr r cos q sin q dy dy dq dq dx dx dq r sin q dr cos q dq r f q r 4 cos 2q dr 8sin 2q dq



View Full Document

Access the best Study Guides, Lecture Notes and Practice Exams

Loading Unlocking...
Login

Join to view Analytic Geometry in Calculus and access 3M+ class-specific study document.

or
We will never post anything without your permission.
Don't have an account?
Sign Up

Join to view Analytic Geometry in Calculus and access 3M+ class-specific study document.

or

By creating an account you agree to our Privacy Policy and Terms Of Use

Already a member?