Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Question
Transcribed Image Text:Sketch the curve and the approximating rectangles for L.
0-1
0-1
-0.5
0-1
-0.5
y
15
-0.5
10
5
y
15
10
5
0-1
(c) Repeat part (a) using midpoints.
M₂ =
M₁ =
Sketch the curve and the approximating rectangles for M₂.
y
15
10
5
y
15
10
5
y
15
10
5
0-1
Sketch the curve and the approximating rectangles for M6.
y
0.5
15
10
0.5
1
0.5
1
1
1
1.5
1
1.5
1.5
2
2
2
2
2
X
X
0-1
0-1 -0.5
0-1
0-1
-0.5
0-1
-0.5
y
15
10
y
15
10
y
15
10
5
y
15
10
5
y
15
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5
y
15
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0.5
0.5
0.5
1
1
1
1
1
1.5
1.5
1.5
2
2
2
2
2
X
X
X
X
X
Transcribed Image Text:(a) Estimate the area under the graph of f(x) = 8 + 2x² from x = -1 to x = 2 using three rectangles and right endpoints.
R₂ =
Then improve your estimate by using six rectangles.
R₂
=
Sketch the curve and the approximating rectangles for R₂.
0-1
0-1
-0.5
y
15
-0.5
0-1
10
5
y
15
0-1
Sketch the curve and the approximating rectangles for R₁.
10
5
y
15
10
5
y
0-1
(b) Repeat part (a) using left endpoints.
43=
4=
y
0.5
15
1
10
15
10
i
5
0.5
1
5
1
Sketch the curve and the approximating rectangles for L₂.
1
1.5
1
1.5
2
X
X
2
X
2
0-1
0-1
0-1
-0.5
0-1 -0.5
y
15
10+
5
y
15
10
5
y
15
10
5
y
15
10
y
15
10
5
0.5
0.5
1
1
1
1
1
1.5
1.5
2
X
2
2
2
X
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