29. If S is the sequence of all rational numbers in the interval [0, 1], enumerated in any way, then lim inf of that sequence

Q: 1-Let B be the set of all infinite sequences over {0, 1}. Is this set countable or not, prove it?

A: Please post the multiple parts separately.Here I answered the 1st question as per our policy.

Q: Use any method to prove that if X = (xn) is a Cauchy sequence of real numbers, then () is also a…

A:

Q: 9. Find the limit (if it exists) of the sequence (x_n) where x_n= n-3n^2.

A: Given xn=n-3n2

Q: Let (sn) be a sequence with lim sup sn = 10 and lim inf sn = 5. (a) Show that (sn) is bounded. (b)…

A: Consider a sequence, Sn, with lim sup Sn = 10 and lim inf Sn = 5. (a) To show that Sn is bounded. By…

Q: Show directly from definition that if a, is a positive real sequence with lim a, = 0 and lim f(r) =…

A: Solve.

Q: Find the limit of the sequence whose terms are given by: a-sub-n = (n^2)(1 - cos(6/n))

A:

Q: (n²)(1 - cos(뉴)). 1.5 COS An

A:

Q: Let Fn be Fibonacci sequence. Prove that:

A: By the definition of the Fibonacci sequence, Fn+2=Fn+1+Fn and the Fibonacci sequence is satisfied…

Q: 8. Prove (from the definition of a limit of a sequence) that if the sequence {a} tends to limit L as…

A: Hi! Thank you for your question.As per guidelines we can solve only one question at a time in case…

Q: Prove that a sequence in ℝ can have at most one limit

A:

Q: The first ten terms of the sequence {2 tan-1 10n}∞n = 1 are roundedto 8 digits right of the decimal…

A:

Q: II. Prove if X and Y are the sequence of real number and converges to x a real number then product…

A: Given that X and Y are the sequence of real number And X and Y converges to x a  real number. The…

Q: 7) Show that if a, > 0, and Lim na, 0, then the series а, + a, + а, + a, + ... diverges.,

A:

Q: Let (X,) be a sequence of real numbers. If for some x e R, (x,) converges to both 7x + 2 and 2x - 13…

A: option  (d)  is correct

Q: Suppose we have a sequence of non-negative real numbers such that each element is strictly less than…

A:

Q: 2. The set of all rational numbers in the interval (0, 1).

A:

Q: 3. Let (Sn) be a sequence of nonnegative real numbers, and suppose lim s, = 0. Prove that lim S, =…

A:

Q: c) Prove that a sequence in R can have at most one limit that is “uniqueness of limits"

A: consider  Xn be a sequence in ℝ

Q: Find the generating function of the sequence {a;}k20 defined by ak = -3 if k even; a = 3 if k odd.…

A:

Q: Let an be the nth term of the sequence 1, 2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6,…

A: The given sequence is 1,2,2,3,3,3,4,4,4,4,..., The first integer 1 occurs in first position. The…

Q: consider the sequence  1, 1/2 ,1, 1/3 ,1 ,1/4, 1,.........  determine the limit superior and limit…

A: Given sequence 1, 1/2 , 1 , 1/3.. The limit superior is 1. As every number of sequence < 1+k for…

Q: Which of the following statements is equivalent to the assertion lim a, = L?Explain. 71. |(a) For…

A:

Q: 8. Consider the sequence {an} such that an+1 = -3 – 2an. Then lim an = -1.

A:

Q: 3. Prove that if (a, } and (b,} are Cauchy sequences of rational numbers satisfying lim (a, - b, = 0…

A: 3.

Q: 8. Suppose that họ, h1, h2, . . . is a sequence défihed as follows: ho = 1, h = 2, h2 = 3, h =…

A: I have given the proof in details

Q: Suppose that the sequence xo, x1, x2... is defined by xo = 6, x1 = 1, and x+2 = 8x+1-15x, for k20.…

A:

Q: Prove or disprove that if a sequence {x,} satisfy x,+1 – xn → 0 then it is Cauchy

A: We have to solve given problem:

Q: b) Set up In rdr as a limit of sums.

A: In this question, concept of Riemann Sum is applied. Riemann Sum To estimate ∫abfxdx , Riemann sums…

Q: Find a sequence of real numbers {a;} such that lim a, does not n-00 xist, but it has 3 subsequential…

A:

Q: Suppose {Pi} and {qi} are sequences of real numbers such that lim pn = p and lim qn = q. Give an e-N…

A: suppose pi and qi are sequences of real numbers such that   limn→∞pn=p  and limn→∞qn=qSo by…

Q: 9. Let {xn}, be a sequence of real numbers. What does the boundedness of this sequence mean?

A: Given xnn=1∞ is a real sequence.

Q: 1 In rdr as a limit of sums. 4 b) Set up

A:

Q: Define a sequence (Sn)n inductively by letting S1 = 1, and Sn+1 = Sn + 1. 1+V5 Prove that lim S, = 2…

A:

Q: Compute the limit n (1+)2n n

A: Taking logarithmic on both sides to evaluate it.

Q: Evaluate the limit of sequence ak  = k-1/k-2

A: We have to find limit

Q: Consider the sequence  1, 1, 2, 1, 2, 3, 1, 2, 3, 4, 1, 2, 3, 4, 5, ... Determine the limit…

A: Here sequence is given derive from.this

Q: Please give an cxample of a sequence (a,) such that: (a) (an) is not bounded above. (b) (an) is not…

A:

Q: Please give an cxample of a sequence (a,) such that: (a) (an) is not bounded above. (b) (an) is not…

A:

Q: Suppose we want to obtain a root of x-x-10 = 0. We can rewrite it as x = √x+10. If we use t…

A:

Q: Suppose {xn} is a bounded sequence. Define bn where lim inf xn :_(n→∞) = lim inf bn :_(n→∞). Show…

A: It is given that xn is the bounded sequence. bn:=infxk: k⩾n Wherelimn→∞infxn:=limn→∞bn To prove bn…

Q: If sequence a_n of positive numbers in increasing, then it is not bounded. TRUE or FALSE

A:

Q: Prove, that (nezond n73) If x"=5,+hen x is not a rational number.

A:

Q: The generating function of the sequence 5,5,5,5,5 is 1-x5 O (1-x) 5 1-5x° O (1-x) 1-125x5 (1-x)…

A: We need to find the generating function of the sequence 5,5,5,5,5.

Q: Let {Sn} n=1 to infinity, be an unbounded sequence of negative numbers. Show {Sn} n=1 to infinity,…

A:

Q: Let an be the nth term of the sequence 1,2, 2, 3, 3, 3, 4, 4, 4, 4, 5, 5, 5, 5, 5, 6, 6, 6, 6, 6, 6,…

A:

Q: Let (x,) be a sequence of real numbers. If for some x e R, (x,) converges to both 7x + 2 and 2x - 13…

A: Which of the following is correct?

Q: how that all the irrational numbers in the interval [0, 1] is dense there.

A:

Q: Give a sequence of positive numbers which is NOT bounded and has exactly one limit point.

A: A real no.p is said to be a limit point if every neighborhood of p contains an infinite no. Of…

Q: Prove that a sequence of positive real numbers {r„}1 tends to 0 if and only if the sequence {},…

A: We have to prove a sequence of positive real numbers xnn=1∞ tends to 0 ⇔ 1xnn=1∞ tends to ∞.

Quadratic Equation

When it comes to the concept of polynomial equations, quadratic equations can be said to be a special case. What does solving a quadratic equation mean? We will understand the quadratics and their types once we are familiar with the polynomial equations and their types.

Demand and Supply Function

The concept of demand and supply is important for various factors. One of them is studying and evaluating the condition of an economy within a given period of time. The analysis or evaluation of the demand side factors are important for the suppliers to understand the consumer behavior. The evaluation of supply side factors is important for the consumers in order to understand that what kind of combination of goods or what kind of goods and services he or she should consume in order to maximize his utility and minimize the cost. Therefore, in microeconomics both of these concepts are extremely important in order to have an idea that what exactly is going on in the economy.