MATH 133 – Calculus with Fundamentals 1 Rates of Change, Slopes of Tangents September 28, 2015

Background

We are now ready to move into Chapter 2 of our text and consider average rates of change, and eventually limits and tangent lines. This is really the start of the subject of calculus itself. Everything we have done up until now has been review of precalculus topics to prepare!

Questions

1) A ball dropped from a height of 40 meters and from a state of rest at time t = 0 has height s(t) = 40 − 4.9t^{2} meters at time t seconds.

(a) How far does the ball travel between t = 1 and t = 1.5? What is the ball’s average velocity over that interval? (Note: Your answer should be negative. That just means the ball is moving downward.)

(b) Complete the following table by following the same steps you did in part (a) for each of the given intervals. Use at least 5 decimal places in all calculations for these.

interval [1, 1.1] [1, 1.01] [1, 1.001] [1, 1.0001]
ave.vel.

(c) Using this information, estimate the velocity of the ball right at the instant t = 1. This is called the instantaneous velocity of the ball at that time.

(d) Now repeat part (b) for these intervals ending at t = 1:

interval [0.9, 1] [0.99, 1] [0.999, 1] [0.9999, 1]
ave.vel.

Are these results consistent with what you did before in part (b)? (They should be!)

2) Do problem 27, parts b,c,d on page 62 in our text. The answer for part (a) would be “percent infected per day.”