152 Activity on Are Length and Surrace AreaNamesThe curve to the left (red) is approximated withlittle segments. Each segment makes a triangle[1]. Each small triangle can be viewed as havingdifferential lengthsSo: ds? = dx + dy?. And ds = dx + dy?As Ax = dx becomes small,Then LidaL= lim EL,miutesectonof curveAx 0preseativehypteneL= f ds.Similarily:L= lim £L,Ay6L= f ds,So, 1.= f dsyour choice of dy/dx or dx/dyify = /(x), asxsbSo, Arc LengthdsL= f dsdsdyifx - 4 y),esysd1. Find the arc length for y = 3x/2 -1 over [0,1]

The given function is: y=3x32-1 To find the arc length of the curve.

The curve to the left (red) is approximated with little segments. Each segment makes a triangle [1]. Each small triangie can be viewed as having differential lengths So: ds? = dx + dy?. And ds = /dx? + dy² As Ax = dx becomes small, Then Lids L= lim EL, L= f ds, i on uve Similarily: L= lim EL, Ay L= f ds, Sa L= f ds your choice of dy/dx or dz/dy So, Arc Length L= f ds ifx - My),csys d 1. Find the are length for y = 3x/2-1 over [0,1] 414

The curve to the left (red) is approximated with little segments. Each segment makes a triangle [1]. Each small triangie can be viewed as having differential lengths So: ds? = dx + dy?. And ds = /dx? + dy² As Ax = dx becomes small, Then Lids L= lim EL, L= f ds, i on uve Similarily: L= lim EL, Ay L= f ds, Sa L= f ds your choice of dy/dx or dz/dy So, Arc Length L= f ds ifx - My),csys d 1. Find the are length for y = 3x/2-1 over [0,1] 414

Elementary Geometry For College Students, 7e

7th Edition

ISBN:9781337614085

Author:Alexander, Daniel C.; Koeberlein, Geralyn M.

Publisher:Alexander, Daniel C.; Koeberlein, Geralyn M.

Chapter9: Surfaces And Solids

Section9.CT: Test

Problem 8CT: Determine whether the statement is true or false. a A right circular cone has exactly two bases. b...

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