(b) Estimate the instantaneous velocity of the pebble when t = 4.

Calculus Stewart (9th edition) Exercises Erratum Fall 2020

1.4 Exercises #23 : Suppose the graphs of f (x) = x² and g(x) = 2^x are drawn on a coor- dinate grid where the unit of measurement is 3 centimeters. Show that at a 1 m distance to the right of the origin, the height of the graph of f is  100

3

2

· 3

100 = 100

3 m but the height of the graph of g is about 2¹⁰⁰³ · 3

10⁵ = 10¹⁰⁰³ log 2 + log 3 − 5 ≈ 324679 km.

2.1 Exercises #5 : The deck of a bridge is suspended 80 meters above a river. If a pebble falls off the side of the bridge, the height, in meters, of the pebble above the water surface after t seconds is given by y = 80 − 4.9t² for 0 ≤ t ≤

r80

4.9 ≈ 4.041 to insure that y = 80 − 4.9t² ≥ 0.

(a) Find the average velocity of the pebble for the time period beginning when t = 4 and lasting

(i) 0.01 seconds.

(ii) 0.005 seconds.

(iii) 0.001 seconds.

(b) Estimate the instantaneous velocity of the pebble when t = 4.