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Calculus II Practice Quiz Exercises

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Math 1B, Calc II, Summer 2020 - Quiz 1. 65 a. Approximate ∫5 𝑓(π‘₯)𝑑π‘₯ using a right approximation with 𝑛 = 3 βˆ†π‘₯ = 𝑏 βˆ’ π‘Ž 65 βˆ’ 5 60 = = = 20 𝑛 3 3 π‘₯0 = 5 π‘₯1 = π‘₯0 + βˆ†π‘₯ = 5 + 20 = 25 π‘₯2 = π‘₯1 + βˆ†π‘₯ = 25 + 20 = 45 π‘₯3 = π‘₯2 + βˆ†π‘₯ = 45 + 20 = 65 For right approximation, we use π‘₯1 , π‘₯2 , & π‘₯3 π‘Ÿπ‘–π‘”β„Žπ‘‘ π‘Žπ‘π‘π‘Ÿπ‘œπ‘₯π‘–π‘šπ‘Žπ‘‘π‘–π‘œπ‘› = 20(𝑓(25) + 𝑓(45) + 𝑓(65)) = 20(44 + 65 + 91) = 4000 ft b. Right approximation on a positive slope (which is the case here) will result in overestimation ...
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