lecture_1 - 18.01 Calculus Jason Starr Fall 2005 Lecture 1....

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18.01 Calculus Jason Starr Fall 2005 Lecture 1. September 8, 2005 Homework. Problem Set 1 Part I: (a)–(e); Part II: Problems 1 and 2. Practice Problems. Course Reader: 1B-1, 1B-2 Textbook: p. 68, Problems 1–7 and 15. 1. Velocity. Displacement is s ( t ). Increment from t 0 to t 0 + Δ t is, Δ s = s ( t 0 + Δ t ) s ( t 0 ) . Average velocity from t 0 to t 0 + Δ t is, Δ s s ( t 0 + Δ t ) s ( t 0 ) v ave = = . Δ t Δ t Velocity , or instantaneous velocity , at t 0 is, v ( t 0 ) = lim v ave = lim s ( t 0 + Δ t ) s ( t 0 ) . Δ t 0 Δ t 0 Δ t This is a derivative , v ( t ) equals s ( t ) = ds/dt . The derivative of velocity is acceleration , a ( t 0 ) = v ( t 0 ) = lim v ( t 0 + Δ t ) v ( t 0 ) . Δ t 0 Δ t Example. For s ( t ) = 5 t 2 + 20 t , ±rst computed velocity at t = 1 is, v (1) = lim 10 t = 10. Δ t 0 Then computed velocity at t = t 0 is, v ( t 0 ) = lim 0 10 t 0 + 10 t = 10 t 0 + 20. Δ
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This note was uploaded on 06/03/2008 for the course MATH B6A taught by Professor Moretti during the Spring '08 term at Bakersfield College.

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lecture_1 - 18.01 Calculus Jason Starr Fall 2005 Lecture 1....

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