There exists a real number R which is greater than 5 O R= {7, 42,2t, and 97/3) O R= {1, 2, and T/6}

Q: If x is any positive integer , then the sum of 6x and 11x is always divisible by what?

A: x is a positive integer. Find sum of 6x and 11x is divisible by what?

Q: There is a real number whose product with every real number equals zero. a. Some has the property…

A: Note: As per company guidelines we are supposed to solve 1 question. So, kindly repost other…

Q: How many solutions are there to the equation X1 + x2 + x3 +x4 + x5 = 21 %3D where r;, i =1, 2, 3, 4,…

A: Depending upon the type of equation, the number of solution will vary. If a system contains linear…

Q: Let c, a, B be nonzero real numbers such that c + B. Find a given that 202n 3 19 - ch 4 ac? с — В WI

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Q: 6. Let r> 2 be an integer. Show that R(2r, 2r) > 2

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Q: Prove the following by proof by contradiction: At least one of the 5 real numbers a, b, c, d, e is…

A: We will use basic properties  of inequality to proof this result by contradiction

Q: f'(x) > O on f1,2) f'(x) 0 on (-3,2)u(2.00) 5"(x)< O on (-00,-3) on (-oo,-3) Lir ontin uous for all…

A: Follow next step

Q: Suppose there is a real number r with the property that r + 1/r is anodd integer. Prove that r is…

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Q: If α and β are two real numbers, we say that β is equivalent to α if there are integers a, b, c, and…

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Q: 4. Let x, y, and z be real numbers. Prove that if x and y are rational numbers and z is an…

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Q: Let n be a real number and let e be a positive real umber. Determine whether there exists a 1 real…

A: Given n be a real number and ε be a positive real number.

Q: For all integers x and y, if 6x+y is odd, then x and y are both odd. True False

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Q: If r and s are real numbers and r < s, then there exists a positive integer t such that r+t = s.…

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Q: Prove that for all positive real a we have 22 +5 20x4 2 4/5. 24 x2 +5

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Q: Find all integers x + 3 such that x – 3 is divisible by x – 3. |

A: To find all integers such that x^3-3 is divisible by x-3

Q: Let æ be a real number. Show that [3r] = [a] + æ + + 3

A: Here we have to show that 3x=x+x+13+x+23

Q: Let c, a, B be nonzero real numbers such that c + B. Find a given that 202n–3 19 cn 4 ac2 n-3 C - B

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Q: 10. (a) Prove: If x and y are real numbers with x < y, then there are infinitely many rational…

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Q: Every odd integer is the sum of three odd integers. There exist an irrational number c and a…

A: True  proof Let us assume  that x is even So x=2z for some constant z Therefore x.y=2zy Which…

Q: By using Caushy Rieman prove that (2) and (3) (2) 4c2) = (3) prove That (3)- 3.

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Q: (a) Find two integers satisfying the equation r³ + 24x² – 2 = 0 mod 23.

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Q: 1. Let x, y, and z be real numbers. Prove the following: [a] -(-x)=x [b] (-x)y = -(xy) and (-xX- y)=…

A: "By Bartleby rules, only first three sub-parts of question 1 have been answered"

Q: There is a positive integer whose square is equal to itself. real а. There is a number m such that…

A: To rewrite the statement in a different way: Firstly, rewrite the statement in the given statement…

Q: We are given non-negative real numbers a1 > a2 > · ·> a2004 such that a1 +a2+•· ·+a2004 <1. Prove…

A: Given non-negative real numbersa1≥a2≥⋯≥a2003≥a2004Anda1+a2+⋯+a2004≤1We have to prove…

Q: Prove that if a > 0, and b is an arbitrary real number then x³ + ax + b= 0 has exactly ne real…

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Q: Let a be a positive real number and let n be an integer greater than 1.Prove or disprove that…

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Q: integer of the form okts is also but not' conversely

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Q: To show that r - 1= In(r-r+ 1) has at least two different positive root in R. 6.

A: We need to analyze the roots of the equation x-1=lnx2-x+1. This equation can be re-written as…

Q: Show that for all integers a, b > 0, the number (a + b) – (a O b) is both nonnegative and even.

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Q: What is the definition of z'? Show that if one value of z' is real, then all other values are real.…

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Q: Are there numbers a and b such that |a + b| &gt; |a|+|b|?

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Q: e3x + 6 enx e(n+1)x = 1+ e® + 2 Sx n! (n+ 1)!

A: The given series is : eex=1+ex+e2x2+e3x6+·····+enxn!+en+1xn+1!   Let fx=ex The above function can be…

Q: *3. Suppose x is a real number and > 0. Prove that (x - e, x + e) is a neighborhood of each of its…

A: Given that 'x' is a real number and ε&gt;0. To prove that x-ε, x+ε is a neighborhood of each of its…

Q: Let c, a, B be nonzero real numbers such that c + B. Find a given that 72n-3 Σ17 00 ac? cn 4 c - B…

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Q: a. Show that for any real number x, if x> 1 then | x4 |≤| 23x4 + 8x² + 4x |.

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Q: Let...

A: Given expansion formula is  a+bn=∑nkk=0nan-kbk

Q: An integer x is odd if x2 is odd. Let x, y and z be integers. If x y and y z, then x | z. For any…

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Q: If a , b are two rational numbers such that Va + vb is a rational number, then prove that Vab is…

A: We have given that , a  and  b are two rational numbers  such that  a + b  is a rational number. We…

Q: (Chapter 3.2. Ex.# 49) Show that if fi(x) is O(g1 (x)), f2(x) is O(92(r)), and f2(r) # 0 and g2(r) #…

A: Given: If f1x is ⊝g1x, f2x is ⊝g2x, and f2x≠0 and g2x≠0 for all real numbers x&gt;0.

Q: Every positive integer is the sum of distinct powers of two. F b C e Every positive integer is the…

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Q: Let, a1 = 3, a2 = 4 and for n 2 3, an = 2an-1 +an-2 – 5, express an in terms of n.

A: We will first find the roots of characteristic equation and write general solution of homogeneous…

Q: Show that if f1(x) is O(g1(x)), f2(x) is O(92(x)), and f2(x) # 0 and g2(x) # 0 for all real numbers…

A: Big theta notation is nothing but an order notation that is used to compare the the growth rates or…

Q: For any positive integer n and r = 1,2, ...,n, we have G) = (","') + C" - }). True O False

A: The expression nr can be presented in the factorial form as follows. nr=n!(n-r)!r! The expression…

Q: If a and b are odd positive integers, and the sum of the integers, less than a and greater than b,…

A: Let a and b are odd positive integers, and it is given that sum of integers, less than a and greater…

Q: 11. How many solutions are there to the equation x₁ + X₂ + X3 + X₁ + X5 + x6 = 29, nonnegative…

A: We have given equation: x1+x2+x3+x4+x5+x6=29

Q: prove that if a>4 then (a-2)^2>4

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Q: Show that for all positive integers n and k, (~^)= (-1)^(" + k-1). k

A: The provided information is  (  k-n) Then we prove this (   k-n)=(-n)*(-n-1)*(-n-2)*.....(-n-k+1)k!…

Q: Show that det(A) is (a* – b*)/(a – b), where a +b ab A = 1 a +b ab 1 a +b for a and b any real…

A: Given, A=a+bab01a+bab01a+b