se for all integers nz2, tity = to shaw that for all integer

Q: Prove that if x is a positive real number, then LV]] = [VTJ

A: The floor function or the greatest integer function gives the greatest integer which is less than or…

Q: Do not use a calculator in this question. (4 V5 – 2)? V5 – 1 CamScanner로 스캔하기 Express in the form…

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Q: Let n and m be positive integers. Evaluate >(km+1 – (k – 1)m+') if possible. If not possible, k=1…

A: Write the terms one by one and add them.

Q: What statement could be used to prove that m f n?

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Q: (e) For any nonzero real number z, prove Σ''-1 1-z"

A: The objective is to prove that for any nonzero real number x, ∑i=1nx-1xi=1-x-n

Q: let A= find nu lity (AT) 3. 8. |

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Q: Ive for æ if In(x? – 1) = 0.

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Q: The number ways in which leters. f the word Pananged of in which letters PARET Can be So that R is…

A: Given, PARET- all letters are different number of letter in PARET=5

Q: Find the product and addition of the approximate numbers x, = 32.452 and x, = 24.3595 all of whose…

A: x1=32.452 and x2=24.3595 To Find: a) Product and addition of the approximate numbers. b) Relative…

Q: ind the general so lution of the differlential eguation

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Q: 1. Let H=10 so 100r f (r,b)=[?][?]+1006 . Compute a[2][?]f

A: we have to derivate the given function f(r,b)=100r1+100b .

Q: (In x+2) Simplify further as, + In x

A: We have to simplify the given equation.

Q: Use proof by contradiction to prove that if x + y > 2, then x > 1or y > 1 (or both).

A: The method of contradiction is used to prove a statement or a set of statements. The inverse of the…

Q: For which positive numbers a is it true that ax >= 1+x for all x?

A: Explanation of the solution is given below...

Q: Show that it is not true that for every error 1/m there exists n such that |Ek=1 polt – r/(1 - r)| <…

A: We will show that for every m there does not exist any unique n that works for all r in (0,1)

Q: For ƒ(x) = sin x, find ƒ"(x), ƒ″(x), ƒ‴(x), and ƒ(4)(x). What is ƒ(4n)(x) when n is a nonnegative…

A: Given  f(x)= sinx Lets take first derivative f'(x)= cos(x)f''(x)= -sin (x)f'''(x)=…

Q: For mighe. any integer exyelicsubysoup of osder Show tht /2 has

A: Since, you have posted multiple questions but according to guidelines we will solve first question…

Q: Let filN >N be defined by f(n) = Ź v(d) for all nEl din where r(R) is the number of the positive…

A: A multiplicative function on the set of natural numbers is a function T such that Tnm=T(n)T(m)…

Q: Prae that x4 -5x +3 is ineducible ouer Q

A: Given polynomial is f(x)= x^4 -5x^3 +3

Q: Prove that re" = 3 – x² for some negative value of x. [Hint: Use the IVT]

A: According to the given information it is required to prove that: xex=3−x2 for some negative value of…

Q: Q- Prove the following identities. (a):- 1-0- AV

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Q: Suppose: n ≥ 3 and x,y ∈ Rn , |x - y| = d > 0 and r is some +R, Need to show: 2r = d, there is…

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Q: -a = Y express L and K as expressions of

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Q: Find a counterexample to show that the statement is Falso- Q. (x+)(R-1) のFor all numlbers X.-メくメ %3D…

A: Part (a) -x&lt;xTake x=-1--1≮-11≮-1 Therefore, the given statement is not true for all values of x.

Q: Need help proving this     −z = (−1)z.

A: Same basic concept of Mathematics  Like  (-) *(-) = + (-) *(+) = -

Q: Ex: @ write out the expessien R(n=4) jki in full. wuich aue free and which ane dummy indices ?…

A: We write expression of curvature Tensor

Q: 2 Xi. にく prove thate 2.

A: Given that  We have to prove the given expression:

Q: Show that if n2 -3 is even, then n is odd. Prove by contrapositive For the toolbar, press ALT+F10…

A: We need to prove by contrapositive.  The contrapositive statement of "If p then q" is "If not q then…

Q: Use Green's thearem to evalute where c is the Loundarde of the regian cncdlosed by and for ラメラ0

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Q: In ALMN, LN is extended through point N to point O, m/NLM = (x – 4)°, mZMNO = (4x – 17)°, and m/LMN…

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Q: n! Verify that Ex1+…+xr=n,xi20 r^n for any r, n>1 x1!x2!...xr!

A: Consider the given information. Let n is greater than equal to 1 arbitrary. Use the mathematical…

Q: If 2x³-4x² + x + 1 = 0 so x = 4x² - 2x³ - 1 then x5-x4|<e, X4 = 1.36603, x5 = 1.366024, is the error…

A: Given x4 = 1.36603x5 = 1.366024

Q: II. Prove the following using Direct Proof. 6. If x is an odd number and y is even number, then x +…

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Q: Show that there is exactly one real number t such that eTt + te" 207 + V2021.

A: Let us take an equation: g(x)=t Where g(x) be any function of x In order to show existence of x such…

Q: Let the numbers c1, C2, ... be defined inductively as follows: c1 = 0 and for every n >1 the number…

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Q: O None of these Oe equal to the above Vdows O is equal to the above O is equal to the above 434

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Q: Let, a1 = 3 and for n > 2, an = 2an-1 +1, express an in terms of n. %3D

A: We will find out the required expression in the term of n.

Q: In yz can be written as : 1 In x - In y + In z a O 4 1. In x- In y- Inz b O 4

A: I have Provided this answer in step-2.

Q: Nadia would like to use the AAS Congrue prove that ATIS = AITH. Would knowing th enough information…

A: Given that:

Q: Find integers s and t so that s· 201 + t · 302 = 1 . S %3D

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Q: Let x e R. Use the method of proof by contraposition to prove hat if x² – 6x + 8 > 0, then x > 4 or…

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Q: Q4/ If A = 3 - l: prove A-A-5I = 0

A: Given that: A=213-1

Q: Show that, by det by b2 92 •92 =TT (ai-bi) br b2 b3 an

A: We have to show that det111⋯1b1a1a1⋯a1b1b2a2a2⋮⋮⋮⋮b1b2b3⋯an=∏i=1nai−bi Let us consider the matrix…

Q: Suppose n (a)= 7a + 4, determine a such that n (a) = 39. %3D

A: GIVEN n(a) = 7a+4 and n(a) = 39

Q: uppose that X~N(µ, o²) and that P(X 3.6) = 0.6554, what are the alues of u and o?

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Q: 3, 5x 60(x2 + *), 3 b) Y = In 7.

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Q: How many extensions of g to A are one-to-one? How manu ou

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Q: MN | QP and MQ || NP MQ 32.Given: TH Prove: = NP

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Q: m above, prove that for every real number c>0, there is a 1/N < c.

A: In every real number c, there is integer N which is N &gt; c.

Q: How do I subsitute X= Ztan into Ha):" ) How do I simphtiy asuming Ok Be

A: Solution : We have given a function fx = x4 + x2   To find : Substitute x = 2 tanθ into the given…