Project #36867 - Calculus 2

Here are the questions:


question 1) consider the explicit formula for the following sequence

a) find the first four terms of the sequenece

b) using a calculator make a table with at least 10 terms and determine a plausible value for the limit of the sequence or state that it does not exist.


question 2) determine the sequence An  Converges or diverges. Find the limit if the sequence converges. 

AN = [1 - 9/n]^n 


question 3) evaulate the following geometric sum:

1/2 + 1/8 + 1/32 + 1/128 +...+ 1/8192 

simply answer 


question 4) use intergral test to determine the convergence or divergence of the following series 

£ (infifity on top of series sign, and k=3 on bottom of series sign) 3/ k(ln k)^2


question 5) use the ratio test to determine if the series £ (infinty in too of series and n=1 on bottom of series) n^48^-n converges or diverges.

a) series converges with r = 

b) series diverges with r =

c) ration test is inconclusive because r= 


question6) determine whether the following series converges or diverges :

£ ( infinity on top of series and k=1 on bottom of series) cos piek / k^2



a) find the linear approx polynominal for the following function centered at the given point a

b) find the quadratic approx polynominal for the following centered at the given point b

c) use the polynominals obtained i. Parts a and b to approx the given quantity

f(x) = e^-x , a=0; approximate e^-0.6


question 8) determine the radius of convergence of the following power series. Then test the endpoints to determine the interval of convergence:

£ k^2 (x+4)^2k / k!

a) the interval of convergence is

b) the radius of convergence is R = 


question 9) 

a) find the first four nonzero terms of the Maclaurin series for the given function

b) write the power series using summation notation 

c) determine the interval of convergence of the series 

f(x)= (-1 + 5x)^-1


thanks if you can have it for me in 50mins 

Subject Mathematics
Due By (Pacific Time) 07/31/2014 01:40 pm
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