Alternating Series

10.1, 10.2 Sequences Tuesday, June 22, 2021 6:02 PM New Section 1 Page 1 New Section 1 Page 2 New Section 1 Page 3 New Section 1 Page 4 New Section 1 Page 5 New Section 1 Page 6 New Section 1 Page 7 10.5, 10.6 Comparison Tests, Alternating Series Tuesday, July 6, 2021 6:02 PM New Section 1 Page 1 New Section 1 Page 2 New Section 1 Page 3 New Section 1 Page 4 New Section 1 Page 5 New Section 1 Page 6 New Section 1 Page 7 New Section 1 Page 8 New Section 1 Page 9 New Section 1 Page 10 11.2 Power Series Thursday, July 15, 2021 6:02 PM New Section 1 Page 1 New Section 1 Page 2 New Section 1 Page 3 New Section 1 Page 4 New Section 1 Page 5 New Section 1 Page 6 New Section 1 Page 7 New Section 1 Page 8 New Section 1 Page 9 New Section 1 Page 10 New Section 1 Page 11 11.3 Taylor, MacLaurin Series Tuesday, July 20, 2021 6:03 PM New Section 1 Page 1 New Section 1 Page 2 New Section 1 Page 3 New Section 1 Page 4 New Section 1 Page 5 New Section 1 Page 6 New Section 1 Page 7 New Section 1 Page 8 New Section 1 Page 9 CALCULUS – II EXAM – V (Su21) NAME (all work must be clearly shown and explained step by step by the methods discussed in class, otherwise it will be considered as an app work, and no credit will be given. Give yourself enough time so that you can upload your work. I will only accept the work under the assignment link, so don’t email me your work.) 1. Find the corresponding rectangular equation of the curve given by 𝑥 = 4 𝑐𝑜𝑠 𝑡 − 1, 𝑦 = 3 + 5 𝑠𝑖𝑛 𝑡 , 0 ≤ 𝑡 ≤ 2𝜋 then graph. Find an equation of the tangent line to the graph at the point where 𝑡 = 𝜋/6. 2. Find the length of the curve given by: 𝑥 = 𝑒 4𝑡 𝑐𝑜𝑠𝑡, 𝑦 = 𝑒 4𝑡 𝑠𝑖𝑛 𝑡 , 0 ≤ 𝑡 ≤ 𝜋/2 3. Graph and find the area of the region bounded by 𝑟 = 8 𝑠𝑖𝑛 2 𝜃 4. Sketch and calculate the distance around the curve given by 𝑟 = 5 − 5 𝑐𝑜𝑠 𝜃 5. Graph and find the slope of the tangent line to the graph of 𝑟 = 8 + 8 𝑠𝑖𝑛 𝜃 at the point where 𝜃 = 𝜋/4 6. Find the length of the curve given by: 𝑥 = 10 𝑐𝑜𝑠 3 𝑡 , 𝑦 = 10 𝑠𝑖𝑛3 𝑡 , 0 ≤ 𝑡 ≤ 2𝜋. 7. Find the corresponding rectangular equation of the curve given by: 𝑥 = 6 𝑠𝑒𝑐 𝑡 − 2, 𝑦 = 4 𝑡𝑎𝑛 𝑡 + 1 then graph. Find an equation of the tangent line to the graph at the point where 𝑡 = 𝜋/4. 8. Find the area of the surface obtained by revolving the region bounded by: 𝑟 = 2 + 2 𝑠𝑖𝑛 𝜃 , 0 ≤ 𝑡 ≤ 𝜋/2 𝑎𝑏𝑜𝑢𝑡 𝑡ℎ𝑒 𝑙𝑖𝑛𝑒 𝜃 = 𝜋/2 9. Graph and find the area of the region enclosed by: 𝑟 = 6 𝑠𝑖𝑛3 𝜃 10. Find the length of the cycloid 𝑥 = 6(𝑡 − 𝑠𝑖𝑛 𝑡), 𝑦 = 6(1 − 𝑐𝑜𝑠 𝑡) 𝑜𝑛 [0 2𝜋] 11. Find the area of the surface generated by revolving the curve 𝑥 = 8 𝑐𝑜𝑠 3 𝑡 , 𝑦 = 8 𝑠𝑖𝑛3 𝑡 , 0 ≤ 𝑡 ≤ 𝜋 about the x-axis axis. 12. Find the length of the curve given by: 𝑥 = 𝑒 𝑡 𝑠𝑖𝑛4𝑡, 𝑦 = 𝑒 𝑡 𝑐𝑜𝑠4𝑡, 0 ≤ 𝑡 ≤ 𝜋/2
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