Calculus: Early Transcendentals 8th Edition

Published by Cengage Learning
ISBN 10: 1285741552
ISBN 13: 978-1-28574-155-0

Chapter 14 - Section 14.2 - Limits and Continuity - 14.2 Exercise: 2

Answer

(a) Continuous (b) Discontinuous (c) Discontinuous

Work Step by Step

(a) The outdoor temperature of longitude, latitude and time is continuous. Small changes in longitude, latitude, or time can produce only small changes in temperature, as the temperature does not jump abruptly from one value to another. (b) Elevation is not necessarily continuous or discontinuous. If we think of a cliff with a sudden drop-off, a very small change in longitude or latitude can produce a comparatively large change in elevation, without all the intermediate values being attained. Elevation can jump from one value to another. (c) The cost of a taxi ride is usually discontinuous. The cost normally increases in jumps, so small changes in distance traveled or time can produce a jump in cost. A graph of the function would show breaks in the surface.
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