Calculus questions

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7nef

Mathematics

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i to u سو 4. (6 Points). Use the method of cylindrical shells to find the volume generated by rotating about the linex=-1 the region bounded by the curves y=4-2x, y=0, x=0 2 Sotto de d 2 1.1.2.2014 ال ho llen on the interval 0, 2) 5. (6 Points). Consider the function $(x) = 2xe a) Find the average value, faw, of Rx) fan una Pawn [ 23 Sene") de od Sach b) Find numbers, c, such that fove = f(c). suppose are - then 1910)-2 = 2 ce - 1. 5 Bonus Problem: 6. (6 Points). Multiple Choices: NO PARTIAL CREDIT Circle the letter of the correct answer. (2 Points each). i. The Area of the shaded region below is given by c. 12y-y?)-(y2 - 4y)]dy D. LI(2y-y)-y-4y)] de @L'to-4»)-(28-y?)dy B. 102-4y)-(2y - y?)]dx X Х x=y? - 4y 3.3) ) لا x=2y-y2 ii. The region bounded by the line y = 2-x and the two axes is revolved about the .r-axis. The volume of solid generated, using Cross sections, is 2. (6 Points). Find the area of the region enclosed by the curves 1 y= Vad y = -x, x=9 2 =vxl 17
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