Math 2253 Homework Due Monday, October 29.   Show all work to get credit.

1-6. Write each sum in sigma notation. For each problem, there are many correct answers

1. 6+7+8+9+10     2. 8+8+8+8+8+8+8+8     3. 1/3 + 1/5 +1/7 +1/9 + 1/11     4. 1/3 - 1/5 +1/7 -1/9

5. 7 + 11 + 15 +19 +23     6. 4/12 + 9/14 + 16/16 + 25/18 + 36/20

For problems 7-11, approximate the area between the graph of 1/x and the x-axis from x=1 to x=11 as follows. In each case, show your work, set up a sum in sigma notation, and use a calculator to put your final answer in decimal form.

7. 5 rectangles, upper sum 8.     10 rectangles, upper sum     9. 5 rectangles, lower sum

10. 10 rectangles, lower sum     11. 5 rectangles, midpoint rule

12. Based on your answers above, make an estimate of the actual area in question