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Notation: In this homework, we use the following notations: . In denotes the left Riemann sum using n rectangles . R. denotes the right Riemann sum using n rectangles . M. denotes the midpoint Riemann sum using n rectangles5. (9 points) Write the following sums in sigma notation. (a) (3 points) 5 +7+9+ 11 + . . . + 2n - 1 (b) (3 points) 1- r+r-r+ + (-1)"x (c) (3 points) 5 - 15 + 25 - 35 + .. . + 105 - 1156. (8 points) The rate at which pollution escapes a scrubbing process at a manufacturing plant increases over time as filters and other technologies become less effective. For this example, assume that the rate of pollution (in tons per week) is given by the function r(t) whose graph is pictured below. 5 (a) (3 points) Use the graph to estimate the tons/week value of MA on the interval [0, 4]. 4 r (t ) (b) (2 points) What is the meaning of M, in terms of the pollution discharged by the 3 plant? Hint: Think about the estimation that 2 you used in (a). What are the units of MA? (c) (3 points) Suppose that r(t) = =e t/2 weeks Use the formula for r(t) to compute LA 2 09 4 5 on [0, 4]