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For each of the following graphs, obtain a lower bound L(A) for the area enclosed by the curve by adding the areas of the squares enclosed completely by the curve. Then obtain an upper bound U(A) for 1 the area by adding the areas of the squares enclosed either partially or completely by the curve. (Notice: the squares in the first graph are 1 by 1 squares and the squares in the second graph are by 2 squares.)

For each of the following graphs, obtain a lower bound L(A) for the area enclosed by the curve by adding the areas of the squares enclosed completely by the curve. Then obtain an upper bound U(A) for 1 the area by adding the areas of the squares enclosed either partially or completely by the curve. (Notice: the squares in the first graph are 1 by 1 squares and the squares in the second graph are by 2 squares.)

Advanced Engineering Mathematics
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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For each of the following graphs, obtain a lower bound L(A) for the area enclosed by the curve by adding the areas of the squares enclosed completely by the curve. Then obtain an upper bound U(A) for 1 1 the area by adding the areas of the squares enclosed either partially or completely by the curve. (Notice: the squares in the first graph are 1 by 1 squares and the squares in the second graph are by 2 2 squares.)
Transcribed Image Text:For each of the following graphs, obtain a lower bound L(A) for the area enclosed by the curve by adding the areas of the squares enclosed completely by the curve. Then obtain an upper bound U(A) for 1 1 the area by adding the areas of the squares enclosed either partially or completely by the curve. (Notice: the squares in the first graph are 1 by 1 squares and the squares in the second graph are by 2 2 squares.)
+4 0.5 (a) L(A) (b) U(A) Explain why L(A) gets no smaller while U(A) gets no larger as the squares are subdivided into four boxes of equal area.
Transcribed Image Text:+4 0.5 (a) L(A) (b) U(A) Explain why L(A) gets no smaller while U(A) gets no larger as the squares are subdivided into four boxes of equal area.
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