Prove that if x is real number then L2xd =LxJe bx+!]

Q: Prove that Va - Vb is irrational number if 'a' and 'b’ are prime number?

A: Given To prove that a-b is irrational number if a and b are prime number.

Q: 1. Prove that 7(x – 1) 2.

A: Let, f(x)= ex-7x+7 ,for x≥2. Differentiating both sides with respect to x, f'(x)= ex-7≥0 . This…

Q: Use mathematical Inductlon to prove that for r>0 and any positive Integer

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Q: Prove (kindly provide reason/s) that for any real numbers m and n, (-m) + (-n) = - (m + n)

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Q: Find the least integer n such that (2x^3+x^2logx) is O(x^n).

A: The given expression is 2x3+x2logx. Concept used: Let f and g from the set of integers or the set of…

Q: 3. Prove or disprove (x, y are real numbers a) [x- y] = [x] – by] TRUE FALSE because:

A: Introduction: The integer, that is largest and less than or equal to the number a is known as floor…

Q: LI) Prove that (3

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Q: 2"-1 for positive integers n.

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Q: Prove (kindly provide reason/s) that for any real numbers m and n, (-m ) + ( - n ) = - ( m + n)

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Q: 2. Prove that L(cashkt)= ki 52-K2

A: To prove that  L(cosh(kt))=ss2-k2

Q: Prove that 1+6x-x is always a positive real number if x =3+Ai for some real 33 number 4

A: The given number is  1 + 6x - x2

Q: 6. Show that Vz eC i) z-7 is a real number. ii) (z-2) is a real number.

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Q: 4. Prove that C, = ,C4 (Hint: Algebraically show that the Left Side = Right Side)

A: We know that  Cr n= Crn = Crn = (n)!(r)! × (n-r)!

Q: Prove that -iEnt/th 1(0)

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Q: Prove that if æ is a real number, then [2a] = [x] +

A: If x is a real number then  to prove- 2x=x+x+12 Greatest integer function is denoted by [x] for any…

Q: 9. Prove that there are as many positive real numbers as there are real numbers.

A: Consider the set X and Y. Then we said that |X| = |Y| if there exists bijective function from X to…

Q: Prove that √1+i√3+√1-i√3 = √6

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Q: 2. Prove that V6 is irrational number.

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Q: how to prove √6 is irrational

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Q: (4) Prove that there is no smallest positive real number.

A: I have to prove that there is no smallest positive real number . Suppose that there is a smallest…

Q: Prove (kindly provide reason/s) that for any real numbers m and n, (- m ) + ( - n) = - ( m + n)

A: To prove: -m+-n=-m+n Where m and n are real numbers.

Q: Prove 3√3  is irrational

A: See the attachment.

Q: Provide either a proof or a counterexample for  For all positive real numbers x, x^2 - x ≥ 0

A: According to the given information, it is required to prove the given equality or give a counter…

Q: 5. Prove that if x is an irrational number, then Vx is also irrational. (Domain: positive real…

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Q: prove that √2+√3 is irrational

A: For rational we needed form p by q P and q are integer

Q: let s be positive integer, then (2) + (;) = %3D

A: sC5 = s!/5!*(s-5!) And sC6 = s!/6!*(s-6)!

Q: Prove that (1-x*)у ,-ху, +р'у-0

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Q: : a number is even  if

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Q: 2. Show that (i) tan 48° tan 23° tan 42° tan67° =1

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Q: Prove that (-1+ iB)" + (-1- i3)" has either the velue 2t! or the value if a B any integer (positive,…

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Q: 3. Show that all the irrational numbers in the interval [0, 1] is dense there.

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Q: (3) prove That () 3

A: We have to use z = x + iy.

Q: 2. Let x be irrational real number. Prove that 2x+3 is irrational

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Q: Prove that 2+/3 is irrational

A: Given,          To Prove : 2+3 is irrational.

Q: Use contrapositive to prove that if x, y are positive real numbers, then Vx + y + vã + Vỹ.

A: By using contrapositive we have to prove that if x, y are positive real numbers, then x+y≠x+y.

Q: Suppose x is a real number. Prove that if x 1 then there is a real number y such that y+1 = x. 4-2

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Q: Let x be a real number. Prove by contrapositive that if æ + 7x = 90, then x < 4.

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Q: (b) Prove that 2m ≤ m! + 2 for m ¤ N. (c) For any nonzero real number x, prove ---3 i=1 = 1- x -n

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Q: For any integer m and any real number x, if x is not an integer, then [x]+[m-x] = m-1.

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Q: Suppose that x is a negative real number and that x < 1/x. Prove that x <-1.

A: Since we know for any real number a,b  If a &lt; b then -b &gt; -a

Q: Use contrapositive to prove that if x, y are positive real numbers, then Vx + y # Vã + Vỹ.

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Q: Prove by contradiction that if a sum of three real numbers is less than 30, th at least one of the…

A: We have to prove by contradiction that if a sum of three real number is less than 30, then at least…

Q: Prove Bernouilli's Inequality which states: If x ≥ −1 then (1 + x)” ≥ 1 + nx for all natural numbers…

A: To Prove: Bernoulli's Inequality which states: If x≥-1, then (1+x)n≥1+nx for all natural numbers n

Q: Suppose x is a real number and x is not equal to zero. Prove that if ((x^1/3)+5)/((x^2)+6)=1/x, then…

A: Given that, x is a nonzero real number, and 8 is not a root of given equation.

Q: Suppose x is a real number and x + 0. Prove that if then x 7 8. 2 16

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Q: Prove that if æ is a positive real number, then LV=]] = LVE] %3D

A: Solution: Definition: The Floor function f is a function that takes any real number x and gives…

Q: Prove or Disprove. for any real numbers x and y, |x+y| = |x| + |y|

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Q: 2. Show that for any real number x, if x + 2 > 10, then x? – 14 > 5x. Use direct proof.

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Q: Use a direct proof to show that if x is a real number such that (x – 1)? = 0, then x³ –1 = 0.

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