Homework 2

# Homework 2 - Version 057 Homework 2 Radin(58415 This...

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Version 057 – Homework 2 – Radin – (58415) 1 This print-out should have 23 questions. Multiple-choice questions may continue on the next column or page – find all choices before answering. 001 (part 1 of 3) 10.0 points Below is the graph of a function f . 1 2 3 - 1 - 2 - 3 2 4 6 8 - 2 - 4 - 6 (i) Estimate the definite integral I = integraldisplay 3 3 f ( x ) dx with six equal subintervals using right end- points. 1. I 10 2. I 11 3. I 9 4. I 12 5. I 8 002 (part 2 of 3) 10.0 points (ii) Estimate the definite integral I = integraldisplay 3 3 f ( x ) dx with six equal subintervals using left end- points. 1. I 8 2. I 6 3. I 4 4. I 5 5. I 7 003 (part 3 of 3) 10.0 points (iii) Estimate the definite integral I = integraldisplay 3 3 f ( x ) dx with six equal subintervals using midpoints. 1. I 3 2. I 5 3. I 7 4. I 6 5. I 4 004 10.0 points Express the limit lim n → ∞ n summationdisplay i =1 5 x i sin x i Δ x as a definite integral on the interval [1 , 8]. 1. limit = integraldisplay 8 1 5 sin x dx 2. limit = integraldisplay 1 8 5 sin x dx 3. limit = integraldisplay 1 8 5 x dx 4. limit = integraldisplay 8 1 5 x dx

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Version 057 – Homework 2 – Radin – (58415) 2 5. limit = integraldisplay 8 1 5 x sin x dx 6. limit = integraldisplay 1 8 5 x sin x dx 005 10.0 points For which integral, I , is the expression 1 25 parenleftBigg radicalbigg 1 25 + radicalbigg 2 25 + radicalbigg 3 25 + . . . + radicalbigg 25 25 parenrightBigg a Riemann sum approximation.
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