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Chapter 10.3

Department

MathematicsCourse Code

MATH 2400Professor

Markus SteindlChapter

10.3This

**preview**shows half of the first page. to view the full**3 pages of the document.**Anna Pyle

University of Colorado Fall 2016

MATH2400 Calculus 3

Textbook: CALCULUS concepts & contexts 4 James Stewart

Chapter 10: Arc Length and Curvature

Arc Length

oThe length of a space curve is defined below:

oIt is useful to parametrize curve with respect to arc length because arc length arises naturally

from the shape of the curve and does not depend on a particular coordinate system

Curvature

oA parametrization r(t) is called smooth on an interval I if r’ is continuous and r’(t) is not equal to

0 on I. It is also called smooth if it has a smooth parametrization. This means it has no sharp

corners or cusps.

oIf C is a smooth curve defined by the vector function r, recall that the unity tangent vector T(t) is

given by the equation shown below and represents the direction of the curve

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