Single Variable Calculus: Early Transcendentals, Volume I
Single Variable Calculus: Early Transcendentals, Volume I
8th Edition
ISBN: 9781305270343
Author: James Stewart
Publisher: Cengage Learning
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Concept explainers

Riemann Sum
Riemann Sums is a special type of approximation of the area under a curve by dividing it into multiple simple shapes like rectangles or trapezoids and is used in integrals when finite sums are involved. Figuring out the area of a curve is complex hence t…
Riemann Integral
Bernhard Riemann's integral was the first systematic description of the integral of a function on an interval in the branch of mathematics known as real analysis.
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Chapter 2.7, Problem 61E

(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)?

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