Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN: 9781285741550
Author: James Stewart
Publisher: Cengage Learning
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Sequence and Series
A sequence is defined as a collection of things. Series is defined to sum the things one by one in the sequence. It was invented by German mathematician Carl Friedrich Gauss.
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6 5 4 -0.5 0.5 1.0 1.5 2.0 2.5 The right endpoints of then intervals are Ax(i) where i = 1 to Then substitute Ax = and n = 4 to find the left end points of four intervals. 2 1 Thus, the right end points of four intervals are Ax(i) = (i), where i = 1 to 4. That is, the four right end points of the intervals are and 2. 2 2 Therefore, the four intervals are given as follows. 2] 2
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Transcribed Image Text:6 5 4 -0.5 0.5 1.0 1.5 2.0 2.5 The right endpoints of then intervals are Ax(i) where i = 1 to Then substitute Ax = and n = 4 to find the left end points of four intervals. 2 1 Thus, the right end points of four intervals are Ax(i) = (i), where i = 1 to 4. That is, the four right end points of the intervals are and 2. 2 2 Therefore, the four intervals are given as follows. 2] 2
Step 1 To find two approximations of the area of the region between the graph of the function f(x) = 2x + 2 and the X-axis over the interval [0, 2] using 4 rectangles, first partition the interval [0, 2 ] into n = subintervals. Then the width of each rectangle is given by using the following formula. b — а Ax = Step 2 Therefore, the width of each rectangle is b — а Ax = in - 0 4 1
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Transcribed Image Text:Step 1 To find two approximations of the area of the region between the graph of the function f(x) = 2x + 2 and the X-axis over the interval [0, 2] using 4 rectangles, first partition the interval [0, 2 ] into n = subintervals. Then the width of each rectangle is given by using the following formula. b — а Ax = Step 2 Therefore, the width of each rectangle is b — а Ax = in - 0 4 1
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