lecture_1

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

This preview shows pages 1–2. Sign up to view the full content.

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

This preview has intentionally blurred sections. Sign up to view the full version.

View Full Document
This is the end of the preview. Sign up to access the rest of the document.

## 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.

### Page1 / 3

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

This preview shows document pages 1 - 2. Sign up to view the full document.

View Full Document
Ask a homework question - tutors are online