qiestion a li (1+1)".(a) Define the sequence {b} by b₁ = 2, and for n ≥ 2,Recall that e lim (1+bn = bn-1 +Show that the sequence {bn} converges to e.(b) Let {an} be the sequence defined bydim1+1n!(i) Show that {an} is an increasing sequence.(ii) Show that the sequence {an} is bounded above.(iii) Show that the sequence {an} converges to e².

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Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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ID Gender Major Employ Age MBA_GPA BS GPA Hrs_Studying Works FT 1 1 No Major Unemployed 39 2.82 3.05 3 0 2 1 No Major Full Time 55 3.49 3.45 7 1 3 1 No Major Part Time 43 3.28 3.5 7 0 4 1 No Major Full Time 56 3.25 3.55 7 1 5 1 No Major Full Time 38 3.26 3.3 6 1 6 1 No Major Unemployed 54 2.87 3.05 4 0 7 1 No Major Full Time 30 3.16 3.35 6 1 8 1 No Major Full Time 37 3.4 3.35 6 1 9 1 No Major Part Time 38 2.84 3.05 3 0 10 1 No Major Full Time 42 3.72 3.7 7 1 11 1 No Major Part Time 52 3.22 3.5 7 0 12 1 No Major Full Time 35 3.44 3.55 7 1 13 1 No Major Full Time 37 3.65 3.9 8 1 14 1 No Major Full Time 53 3.02 3.3 6 1 15 1 No Major Part Time 51 3.03 3.25 6 0 16 1 No Major Full Time 40 3.8 3.8 8 1 17 1 No Major Full Time 33 3.23 3.5 7 1 18 1 No Major Part Time 53 3.26 3.5 7 0 19 1 No Major Full Time 43 3.53 3.75 8 1 20 1 No Major Unemployed 35 3.75 3.9 8 0 21 1 No Major Full Time 57 3.15 3.2 6 1 22 1 No Major Part Time 32 3.66 3.75 8 0 23 1 No…
Use the pulse rates in beats per minute (bpm) of a random sample of adult females listed in the data set available below to test the claim that the mean is less than 72 bpm. Use a 0.05 significance level. Click the icon to view the pulse rate data. Assuming all conditions for conducting a hypothesis test are met, what are the null and alternative hypotheses? Ο Α. Ho: μ= 72 bpm H1:µ 72 bpm H1:µ 72 bpm Determine the test statistic. (Round to two decimal places as needed.) Determine the P-value. (Round to three decimal places as needed.) State the final conclusion that addresses the original claim. Ho. There is evidence to conclude that the mean of the population of pulse rates for adult females is 72 bpm.
Base year (2000) Current year (2005) Сommodity Оuantity Price Qиantity Price A 4.00 58500 6.00 62000 B 3.50 15630 5.50 13050 C 3.00 26230 5.00 25000 D 2.50 11360 4.00 10000 E 2.00 30000 3.00 37500 Also it is given that : E P,q, = 455795, E P,q, = 721275, EP,% = 703555, and E P,q, = 468675. 5. Laspaeyre's price index number for 2005 is : (A) 154.36 (B) 136.54 (С) 144.50 (D) 164.36.
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lim (1+1)". (a) Define the sequence {bn} by b₁ = 2, and for n ≥ 2, Recall that e lim bn = bn-1 + Show that the sequence {bn} converges to e. 1 n!