   Chapter 2.7, Problem 61E

Chapter
Section
Textbook Problem

(a) Graph the function f ( x ) = sin x − 1 1000 sin ( 1000 x ) in the viewing rectangle [ – 2π, 2π] by [– 4, 4 ]. What slope does the graph appear to have at the origin?(b) Zoom in to the viewing window [–0.4, 0.4] by [– 0.25, 0.25] and estimate the value of f'(0). Does this agree with your answer from pan (a)?(c) Now zoom in to the viewing window [– 0.008, 0.008] by [– 0.005, 0.005]. Do you wish to revise your estimate for f'(0)?

(a)

To determine

To find: The slope of the graph at the origin.

Explanation

Graph:

Use the online graphic calculator and draw the graph as shown in Figure 1.

(b)

To determine

To estimate: The value of f(0) and does it agree with the answer from part (a).

(c)

To determine

To revise: The estimate for f(0).

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