# AP Calculus BC 2003 Scoring Guidelines Form B

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5 SCORING GUIDELINES (Form B) Questio A particle moves i the xy-plae so that the positio of the particle at ay time t is give by ( ) 7 x t e t e t = + ad ( ) t t y t = e e. (a) Fid the velocity vector for the particle i terms of t, ad fid the speed of the particle at time t =. Fid dy dy i terms of t, ad fid lim. dx t dx (c) Fid each value t at which the lie taget to the path of the particle is horizotal, or explai why oe exists. (d) Fid each value t at which the lie taget to the path of the particle is vertical, or explai why oe exists. 7 (a) x () t = 6e t 7e y () t = 9e + e t t t t 7t t t Velocity vector is < 6e 7 e, 9e + e > : : x( t) : y( t) : speed Speed = x() + y() = ( ) + = dy dy dt 9e + e = = dx dx 6e 7e dt t t t 7t dy : i terms of t dx : limit t t dy 9e + e 9 lim = lim = = dx t t 7t 6e 7e 6 t (c) Need y t t () t =, but 9e + e > for all t, so oe exists. : cosiders y( t) = : explais why oe exists (d) Need x () t = ad y() t. t 7t e = e t e = 6 7 t = l 6 ( ) : cosiders x( t) = : solutio Copyright by College Etrace Examiatio Board. All rights reserved. 5

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