MAC 2283 Study Guide - Midterm Guide: Polar Coordinate System, Xbl, Parallelepiped
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10. 1 curves defined by parametric equations . ex) = -4 y= tea. = yet ( o ) y=xe (x ) Tangents. de?---o horizontal tangent d = % if d =o vertical both -0 ethel 2-64 tangent ltrea area of 4=1-1-4. Eeeb: = fly dx =/? gc-4. fl-4. de/trclength. - length of. Eeeb about x-axis s=f 2elcae(cid:195)2-(de de ex) find the equation of the tangents to the curve. Y= 4-01-2 that pass through the point 40,67 . ( x) til * = iz =- =l l= -4 ( o) 2-0 -6 -14=0 (e-c) (-41-4-2)=0 (t-174-(1-2)=0 e- 1 or -2 { l=x -4. Polar curves . symmetry: about polar axis : same when 0 replaced by -0, about the pole : same when replaced by - r r or o replaced by otto, about o= . : same when o replaced by tc -0. Rzcosczo)= i rcoso=x rsino =l r2(coste - sink) : 1- 2- always the same . n n.
