1. Consider the shaded area below the graph of the function y = x² + 1, above the x-axis and between the lines r = -1 and r = 1, illustrated below. y = a² + 1 -1.5 -1 -0.5 0.5 1 1.5 (a) Use n = 4 rectangles and left endpoints for each rectangle to estimate the shaded area. Notice that you cannot be certain whether this estimate is an overestimate or an underestimate because some rectangles miss shaded area and other rectangles include unshaded area. (b) Use n = 4 rectangles and choose your sampled point to guarantee that you get an overestimate of the shaded area. (c) Use n = 5 rectangles and choose your sampled points to guarantee that you get an underestimate of the shaded area. 2.
1. Consider the shaded area below the graph of the function y = x² + 1, above the x-axis and between the lines r = -1 and r = 1, illustrated below. y = a² + 1 -1.5 -1 -0.5 0.5 1 1.5 (a) Use n = 4 rectangles and left endpoints for each rectangle to estimate the shaded area. Notice that you cannot be certain whether this estimate is an overestimate or an underestimate because some rectangles miss shaded area and other rectangles include unshaded area. (b) Use n = 4 rectangles and choose your sampled point to guarantee that you get an overestimate of the shaded area. (c) Use n = 5 rectangles and choose your sampled points to guarantee that you get an underestimate of the shaded area. 2.
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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Transcribed Image Text:1. Consider the shaded area below the graph of the function y = x² + 1, above the x-axis
and between the lines r = -1 and r = 1, illustrated below.
y = a² + 1
-1.5
-1
-0.5
0,5
1
1.5
(a) Use n = 4 rectangles and left endpoints for each rectangle to estimate the shaded
area. Notice that you cannot be certain whether this estimate is an overestimate
or an underestimate because some rectangles miss shaded area and other rectangles
include unshaded area.
(b) Use n = 4 rectangles and choose your sampled point to guarantee that you get an
overestimate of the shaded area.
(c) Use n = 5 rectangles and choose your sampled points to guarantee that you get an
underestimate of the shaded area.
2.
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