Final Review Sheet - a CHAPTER 12| comp b= a b a a2 a ab...

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CHAPTER 12 || ¿ a ¿ comp a b = a∙b ¿ || ¿ a ¿ 2 a proj a b = a∙b ¿ || τ = r× F || ¿ a×b ¿ a ¿ b sin θ || a 2 b 3 a 3 b 2 ,a 3 b 1 a 1 b 3 ,a 1 b 2 a 2 b 1 || r = r ο + tv a ( x x ο )+ b ( y y ο )+ c ( z z ο )= 0, ax + by + cz + d = 0 || ¿ ax 1 + b y 1 + c z 1 + d ¿ D p→ pl = ¿ Ellipsoid x 2 + y 2 + z 2 = 1 Cone x 2 + y 2 = z 2 Cylinder x 2 + y 2 = 1 Hyperboloid of 1 Sheet x 2 + y 2 z 2 = 1 Hyperboloid of 2 Sheets x 2 y 2 z 2 = 1 Elliptic Paraboloid x 2 + y 2 = z Hyperbolic Paraboloid x 2 y 2 = z CHAPTER 13 || x = cos t , y = sin t || L = a b || ¿ r' ( t )∨ ¿ T ( t )= r ' ( t ) ¿ || s ( t )= a t ¿ r' ( u )∨ du = a t || ¿ T ' ( t )∨ ¿ N ( t )= T ' ( t ) ¿ || κ ( t )= ¿ T ' ( t ) r' ( t ) ¿ ,a=V’T+kV*VN || B ( t )= N ( t ) ×T ( t ) CHAPTER 14 || lim ¿ ( x , y ) ( a,b ) f ( x , y )= L ¿ if for every ε>0 there is also δ>0 such that 0 < , then ¿ f ( x , y )− L ¿ ε Taking limits.. approach lines such as x,y axis. Approach lines such as y=x 3 , x=y, etc. Continuity: sandwich theorem; if g ( x , y ) ≤ f ( x, y ) ≤h ( x , y ) , then the limit will be between those two functions.
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