2414 - HW Assn 8
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Mathematics
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Apr 3, 2024
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Uploaded by BaronTankGull47
MATH 2414 — HW Assignment 8 (Sections 9.2 — 9.9 but primarily 9.4 —9.9) 1. Which of the following converges? A Y(4+ ) B) §:§% o (3 E) Zcos(n) cos(nn 2. Determine if the alternating series \/— converges or diverges. If it converges, determine if the series converges absolutely or condntlonally. A) Diverges B) Absolutely convergent C) Conditionally convergent
3. Use the Limit Comparison Test to determine convergence or divergence of the following series by 3 n/2—7 3%+ 6n+5 choosing the correct comparison series: E A) Diverges by comparison with E —y' n 2 % B) Converges by comparison with n C) Diverges by comparison with 37 - 2 % D) Converges by comparison with E 7 & E) Converges by comparison with 1/ 2 7 o0 . . —n 4. Which of the following test(s) could be used to show the convergence of E € 1 n A) (1) Integral Test B) (2) Ratio Test C) (3) Root Test D) (4) Geometric Series Test E) Both (1) and (4) are correct F) Both(2) and (3) are correct G) (1),(2),(3), and (4) are all correct
n 8n’+ 6n* — 7 5. Which test(s) could be used to show that E converges? A) (1) Ratio Test B) (2) Limit Comparison Test C) (3) P-Series Test D) Both (1) and (2) are correct E) Both (1) and (3) are correct F) (1),(2), and (3) are all correct o0 Z Inn 6. Determine which of the following tests could be used to show the divergence of p— n n=3 A) (1) Integral Test B) (2) Direct Comparison Test C) (3) Nth-Term Test for Divergence D) Both (1) and (2) are correct E) Both(2) and (3) are correct F) (1),(2), and (3) are all correct 7. Find the fourth degree Taylor polynomial centered at ¢ = 9 for the function. f(x)=Inx A) In9+9(x-9)-162(x-9)* +2187(x-9)’ —26244(x -9)* | | . | | B) In9——(x-9)+—(x-9)Y ———(x-9)' + x-9)* ) 9( ) 162( ) 2187( ) 26244( ) | | . | 1 C) In9—-——(x-9)———(x-9)" - x=9) = ) 9( ) 162( ) 2187( ) 26244 | | ” | | D) In9+—(x-9)-—(x-9) + ——(x-9)’ - ) 9( ) 162( ) 2187( ) 26244 E) In9-9(x-9)+162(x-9)" -2187(x-9)" +26244(x-9)" (x-9)' (x-9)’
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8. Find the radius of convergence of the power series. i (6x)7" n=0 (2")' A) O B) 6 C) 12 D) 36 E) o 9. Find the interval of convergence of the power series. (Be sure to include a check for convergence at the endpoints of the interval.) 53) A) [-9,9) B) (-9.,9) c) [-9.9] oy [-L1 L 99) (1 1) E) |-=— ' 99,
10. Use the power series to determine a power series, centered at O, for the function. Identify the interval of convergence. f(x)= 4x* +1 O a) 34, xe(-1) O b) g(—l)"f’x’”,xe(—l:l) O ¢ é(-l)"2"x2",x6(-2,2) O q) Z( 1)"2"x", xe[ %%) Oe)m_nn.ln__ll) g( )"4"x ,AG( S