Dr. Knisley

Review for Exam 3

Show your work and/or explain your answers.
  1. Evaluate the limit

    2. lim
    n® ¥    		 n2+e-n
    ( n+1) 2
  2. Find the general term for the recursion
    3. yn+1 =  1
    2    		 yn+ 1
    2
    Does the recursion have a limit? If so, what is it?
  3. John invests $1000 initially in mutual funds and then $100 per month thereafter. If the investments value increases by 1% each month, how much will John's investment be worth in 10 years?
  4. Use geometric series to write the following decimal as a rational number: 0.030303¼
  5. Use geometric series to determine what the series converges to and for what values of x it converges:
    6. 1+cos( x) +cos2( x) +¼+cosn(x) +¼
  6. Use the integral test to determine if the following series converges or diverges:
    7. ¥
    å
    n = 1    		 n
    en
  7. Know how to find the Fourier coefficients for the assigned homework problems in section 7.5. Test problems from 7.5 will come from those problems.
  8. Sketch the graph of what the Fourier series of
    9. f( x) =  ì
    ï
    ï
    ï
    ï
    í
    ï
    ï
    ï
    ï
    î
    2 
    if
    | x| £ p
    2
    0 
    if
    | x| >  p
    2
    converges to on [ -p,p] . What does it converge to on [ -3p,3p] ?
  9. Determine if the following series converges using the comparison test:
    10. ¥
    å
    n = 1    		 n
    en    +n
  10. Determine if the following series converges absolutely:
    11. ¥
    å
    n = 1    		 ( -1) nn
    en    +n
  11. Determine if the following series converges uniformly on [ -p,p]
    12. ¥
    å
    n = 1    		 sin( nx) 
    n2+1