Quiz 7 2014 Answers - Arts Science 1D06 Quiz#7 29 January 2015 1:30 pm Full Name Student TA Please provide detailed solutions to the problems below

Quiz 7 2014 Answers - Arts Science 1D06 Quiz#7 29 January...

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Arts & Science 1D06 Quiz #7 29 January 2015 1:30 pm Full Name: Student # : TA: Please provide detailed solutions to the problems below. Correct responses without justification may not receive full credit. The use of a calculator is permitted. 1. Determine the type of each of the following improper integrals (circle your choice(s)) and whether[6]each is divergent or convergent.Evaluate those that are convergent.Hint:Type 1 improperintegrals have an infinite interval and Type 2 improper integrals have discontinuous integrands.(a)integraldisplay40xx2-4dxType: 1 , 2(b)integraldisplay31x2x2-9dxType: 1 , 2You may use thatintegraltext1x2x2-9dx=x2-99x+C(c)integraldisplay0e-x(1-x)dxType: 1 , 2 Hint: integrate by parts.
2. Use the comparison test for improper integrals to show thatintegraldisplay1exxdxdiverges.[2] 0 3. Consider the region bounded by the curvesy=+1-x2andy=|3x| -3.[4](a) Sketch the enclosed region.

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