Comparison Tests

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 10.3, 10.4 Series Tuesday, June 29, 2021 6:04 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 New Section 1 Page 12 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 (Su21) EXAM – IV (all work must be clearly shown and explained step by step, 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.) (π‘₯βˆ’2)𝑛 1. Find the interval of convergence of the power series βˆ‘βˆž 𝑛=1 4 βˆšπ‘›+3 4 2. Find the 6-th Taylor polynomial of 𝑓(π‘₯) = √π‘₯ centered at c = 1, and use the polynomial to 4 approximate √1.4. 4 3. Find a power series centered at c = 3 for 𝑔(π‘₯) = 9βˆ’2π‘₯ 3 4. Find the MacLaurin series of 𝑔(π‘₯) = 𝑒 2π‘₯ then of 𝑓(π‘₯) = 𝑒 βˆ’2π‘₯ . Use the first six terms of the 3 1 last series to approximate ∫0 𝑒 βˆ’2π‘₯ 𝑑π‘₯ 5. Find the interval of convergence of the power series βˆ‘βˆž 𝑛=1 (π‘₯+1)𝑛 𝑛4 +2 𝑛! 6. Use the Ratio Test to determine the convergence of βˆ‘βˆž 𝑛=0 𝑛𝑛 7. Find a Maclaurin series of 𝑔(π‘₯) = π‘π‘œπ‘  π‘₯ π‘‘β„Žπ‘’π‘› π‘“π‘œπ‘Ÿ π‘π‘œπ‘ ( π‘₯ 5 ). Use the first five terms of 1 the series to approximate ∫0 π‘π‘œπ‘ ( π‘₯ 5 )𝑑π‘₯ 11 8. Find a power series centered at c = -4 for 𝑔(π‘₯) = 16+3π‘₯ 𝑛 9. Use the Root Test to determine the convergence of: βˆ‘βˆž 𝑛=1(1 βˆ’ 7/𝑛) . If the test fails, use a different one. 1 1 10. Find a power series representation for 𝑓(π‘₯) = 1+π‘₯ then for 𝑓(π‘₯) = 1+π‘₯ 2 , and use the first 1 seven terms of the appropriate series to approximate ∫0 π‘Žπ‘Ÿπ‘π‘‘π‘Žπ‘›( π‘₯ 4 )𝑑π‘₯. 11. Find a Maclaurin series of 𝑔(π‘₯) = 𝑠𝑖𝑛 π‘₯ π‘‘β„Žπ‘’π‘› π‘“π‘œπ‘Ÿ 𝑠𝑖𝑛( π‘₯ 6 ). Use the first five terms of 1 the series to approximate ∫0 𝑠𝑖𝑛( π‘₯ 6 )𝑑π‘₯ 12. Find the 6-th Taylor polynomial of 𝑓(π‘₯) = √π‘₯ centered at c = 9, and use the polynomial to approximate √9.5
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