School

Boston UniversityDepartment

Mathematics & StatisticsCourse Code

CAS MA 123Professor

John BergdallStudy Guide

FinalThis

**preview**shows pages 1-3. to view the full**65 pages of the document.**MA 123 – Calculus I

Final Exam Study Guide

University of Boston – Fall 2015

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MA 123 - Lecture 1 - Limits

Limits:

●developed in the 19th century by Cauchy

●measure both velocity and area which are defined using limits and approximations

●fundamental theorem of calculus correlates to the rate of change = area

●computing velocity is a basic problem

Question 1:

From start to end, how fast was the car going?

Answer:

Velocity =

Distance

Time

or V =

D

T

Average Velocity=

Distance Traveled

Time Elapsed

=

rise

run

= slope of the line

Car is moving

Distance

Distance

Traveled

Positio

n

Time

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MA123 - Lecture 2 - Limits Continued

Average Velocity:

●Take an equation of motion P(t)

●The average velocity from time #1 to time #2 equals

position at time 2 - position at time 1

time 2 - time 1

Question:

How do you compute instantaneous velocity?

Answer:

●The idea is to fix one time of interest, T0, let the second time vary

●The instantaneous velocity at T0 is approximately the average velocity from time T0 to

another time.

P(t

)

t

T1 T2

(T1,P(T1)) Slope = Average Velocity

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