Use six rectangles to find an estimate of each type for the area under the given graph of $f$ from $x = 0$ to $x = 12$. 1. Take the sample points from the left-endpoints. Answer: $L_6 = $ 2. Is your estimate $L_6$ an underestimate or overestimate of the true area? Overestimate 3. Take the sample points from the right-endpoints. Answer: $R_6 = $ 4. Is your estimate $R_6$ an underestimate or overestimate of the true area? Underestimate 5. Take the sample points from the midpoints. Answer: $M_6 = $
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Use six rectangles to find an estimate of each type for the area under the given graph of f from x = 0 to x = 12. 1. Take the sample points from the left-endpoints. Answer: L6 2. Is your estimate L6 an underestimate or overestimate of the true area? Choose one 3. Take the sample points from the right-endpoints. Answer: R6 4. Is your estimate R6 an underestimate or overestimate of the true area? Choose one 5. Take the sample points from the midpoints. Answer: M6 Note: You can click on the graph to enlarge the image.
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Consider the following. (a) Use six rectangles to find estimates of each type for the area under the given graph of f from x = 0 to x = 36. (i) Sample points are left endpoints. L6 (ii) Sample points are right endpoints. R6 (iii) Sample points are midpoints. M6 (b) Is L6 an underestimate or overestimate of the true area? overestimate underestimate (c) Is R6 an underestimate or overestimate of the true area? overestimate underestimate (d) Which of the numbers gives the best estimate? R6 L6
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(a) Use six rectangles to find estimates of each type for the area under the given graph of $ f $ from $ x = 0 $ to $ x = 12 $. (i) $ L_{6} $ (sample points are left endpoints) (ii) $ R_{6} $ (sample points are right endpoints) (iii) $ M_{6} $ (sample points are midpoints) (b) Is $ L_{6} $ an underestimate or overestimate of the true area? (c) Is $ R_{6} $ an underestimate or overestimate of the true area? (d) Which of the numbers $ L_{6} $, $ R_{6} $, or $ M_{6} $ gives the best estimate? Explain.
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