Project #2797 - calculus hw help

Will send the work where its readable, calculus 2

Show all work and leave all answers as exact answers (do NOT estimate with a calculator).

  1. Findthegreatestlowerboundandleastupperboundofthefollowingsets(provided they exist).

    (a) (2,5)∪{5.1,5.01,5.001,5.0001,...} (b) {xR|sinx=cosxandx0}

    (c) {xR||x5|>2}

  2. Determine if the sequence is monotone and justify your answer. State what type of

    specific behavior it exhibits (increasing, nondecreasing, etc.). (a) an = n

page1image6168

3n
(b) an =(1)n 3 n

page1image7528

3. Determine if the following sequences converge or diverge. If a sequence converges, find its limit.

(a) an = sin2 n. n

(b) an = 2n n2

(c)an= n5n
􏶕 2􏶖n/2

(d) an = 1 + n
4. Use L’Hopital’s Rule to find the following limits (of sequences or functions).

page1image11736 page1image11896 page1image12056 page1image12216

(a) lim (b) lim

n+3 n→∞ n2 +5n+6

page1image13720

􏶕n+2􏶖n n→∞ n1

page1image14512

(c) limln(x)ln(sinx). x0+

(d) limxsinx x0+

5. Find lim sin(aθ) for real numbers a, b > 0. θ0 bθ

page1image16584

6. (Exploration,nottobegraded)Writethefollowingsequenceasarecursivesequence (the n-th term gn in terms of the (n-1)-th term gn1).

1,2=1+1,1+1,1+ 1 ,1+ 1 ,... 121+11+1

page2image2040 page2image2200 page2image2360 page2image2520 page2image2680 page2image2840

2 1+1 2

page2image3632
  1. (a)  Write the first 5 terms g1, ..., g5 as rational numbers.

  2. (b)  Use a calculator, MS excel (this is most efficient), or some other program to

    compute the first 25 values (to at least 10 decimals) of {gn}.

  3. (c)  Is the sequence monotone?

  4. (d)  Multiply the 25th term by 2, subtract 1, and then square it. What integer is this near?

  5. (e)  What (irrational number) do you now expect the sequence to converge to? The limit is a very famous number called the golden ratio (google it!)

  6. (f)  The Fibonacci sequence is given by the recursive formula f1 = 1, f2 = 1, and

    fn = fn1 + fn2 for n 2. Compare the sequences gn and an = fn+1 . fn

page2image10984

Subject Mathematics
Due By (Pacific Time) 03/01/2013 02:00 am
Report DMCA
TutorRating
pallavi

Chat Now!

out of 1971 reviews
More..
amosmm

Chat Now!

out of 766 reviews
More..
PhyzKyd

Chat Now!

out of 1164 reviews
More..
rajdeep77

Chat Now!

out of 721 reviews
More..
sctys

Chat Now!

out of 1600 reviews
More..
sharadgreen

Chat Now!

out of 770 reviews
More..
topnotcher

Chat Now!

out of 766 reviews
More..
XXXIAO

Chat Now!

out of 680 reviews
More..
All Rights Reserved. Copyright by AceMyHW.com - Copyright Policy