calculus 2 read below carefully

zmxmw
timer Asked: Dec 11th, 2017

Question Description

read carefully

i don't need the answers for these numbers

i want you to make me steps so when i get the same questions with different numbers i will follow a certain steps to get the right answer no matter what the numbers are.

and please name the formulas that you are going to use and explain everything.

do all these for the 7 questions

(zoom in to read the picture )


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Exercise1:a)Decide whether or not the improper integral converges or diverges. Compute the sum if it converges. So lnx dx b)investigate the convergence of the improper integral +x2 2x+(x)2+2 Exercise2:A bottle of soda pop at room temperature (72°F) is placed in a refrigerator where the temperature is 44°F. After half an hour the soda pop has cooled to 61° F. a) What is the temperature of the soda pop after another half hour? b) How long does it take for the soda pop to cool to 50°F. Exercise3.a)For What values of r does the function y = e' satisfies the differential equation: 3y" + 2y' - 5y = 0? b)if ri and r2 are the values of r found in part a) show that every y in the family of functions y = aeri* + berx is also a solution. Exercise 4:Solve the initial value problem using separation of variable method. dy t+tcost at y y(0) = 1 Exercise5:a)Use the integral test to decide whether or not the series converges or diverges: 1 In=1 nin(n) b)Use the ration test to decide whether or not the series is convergent or divergent (n) ! c)Use comparison test or limit comparison test to decide about the convergence of the series: 2n4 +4n+1 En=1 (3n+1) In=1 / 12 tn Exercise6:Find the interval of convergence and the radius of convergence of the power series: (-1) n2(x - 2) Σ E 3n n=0 x² Exercise7: a) Find the MacLaurin Series of the function 27-43 using the MacLaurin series of 1-x-cos(x)+sin(x) b)Use series to find the Limit lim x- 1+x-ex
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