Q1. Show that the following sequences of sets, {Ck}, are
nondecreasing,
then find limk→∞ Ck.
(a) Ck = {x: 1/k ≤ x < 100 − 1/k}, k = 1, 2, 3, . . . .
(b) Ck = {(x, y): 1/k ≤ x2 + y2 ≤ 1 –
(1/k)}, k = 1, 2, 3 . . .
Find a closed formula for each of the following sequences. Show
all work and explain your answers.
(a) {1, 6, 17, 34, 57, 86, 121, . . .}, where
a0 = 1.
(b) an = 5an−1 + 4, a0
= 2
(c) an = 10an−1 −
21an−2, a0 = 6, a1 =
26.
The following sequences show the wildtype and mutant alleles of
part of a gene. What is the name of this type of mutation?
Wildtype DNA: 5’
AAC – AGC –
CTG – CGT – ACG – GCT – CTC 3’
Wildtype protein: Asn – Ser – Leu – Arg – Thr – Ala – Leu
Mutant
DNA: 5’ AAC –
AGC – CTG – CTT – ACG – GCT – CTC 3’
Mutant protein: Asn – Ser –...
1. Use the midpoint of each subinterval for the value of each ck
to find the Riemann sum S5S5 for the following information. Round
your answer to the nearest hundredth.
f(x)=49−x^2 [a,b]=[−7,3]; n=5
2. Find the Riemann sum S5S5 for the following information.
Round your answer to the nearest hundredth.
(x)=sqrt5−x; [a,b]=[−5,5]; n=5, c1=−4.5, c2=−2.5,c3=−0.5,
c4=1.5, c5=3.5
For each of the following sequences find a functionansuch that
the sequence is a1, a2, a3, . . ..
You're looking for a closed form - in particular, your answer
may NOT be a recurrence (it may not involveany otherai). Also,
while in general it is acceptable to use a "by cases"/piecewise
definition, for this task you must instead present a SINGLE
function that works for all cases.(Hint: you may find it helpful to
first look at the sequence of...
Find sequences that satisfy the following or explain why no such
sequence exists:
a) A sequence with subsequences converging to 1, 2, and 3.
b) A sequence that is bounded above, but has no convergent
subsequence.
c) A sequence that has a convergent subsequence but is unbounded
(note: unbounded
means not bounded below or not bounded
above.
d) A sequence that is monotonic and bounded, but does not
converge.
1. Find the 100th and the nth term for each of the following
sequences.
a. 50,90,130,...
b. 1,4,16,...
c. 7, 74,77,710,...
d. 197+7x327, 197+8x327,
197+9x327,...
2. Find the first five terms in sequences with the following nth
terms.
a. 10n-5
b.2n-1
3. How many terms are there in each of the following
sequences?
a. 11,15,19,23,...331
b. 59,60,61,62,...459
1.) Find the 100th and the nth term for each of the following
sequences.
a. 1,3,5,7,...
b.70,100,130...
c.1,3,9...
d.8,84,87,810,...
e. 200+6x231, 200+7x231,
200+8x231
2. Find the first five terms in sequences with the following nth
terms.
a. 2n2+6
b.4n+1
c. 10n-5
d.2n-1
find a patternin the following sequences and write the
next two terms. classify each seqences as arithmetic geometic or
neither
1,4,16,64,
and 3,6,9,12
Chui-Kee Limited (CK) is a limited liability company
incorporated in Hong Kong. CK has a chain of Chinese restaurants
specialised in seafood dishes. It operates eight restaurants, and
they are located in popular shopping districts, like Central,
Causeway Bay, Mongkok and Tsim Sha Tsui. CK is famous for its spicy
seafood cuisine, and its restaurants are popular among tourists and
local citizens. You are the Audit Manager of Moon CPA Limited
(Moon). You are responsible for the financial statements audit...