a – b -| < 1, if|a| < 1, and |b| < 1. 1- āb - Show that|-

Q: B) Let f:R - R be defined by. 3 if x rational number. f(x) = if x irrational number !3! Show that f…

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Q: = 1+ x+x?. . Show that ifx is se smail that x and higher powers can be neglected, then:

A: Note : Since you have asked multiple question, we will solve the first question for you.

Q: Find all values of x such that fx>0 and all x such that fx<0

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Q: 4. Let IR be the set of all real numbers, xER and n EN such that n 2 2. If (1+x)> 0, prove that Pn :…

A: Let ℝ be the set of all real numbers,  Let x∈ℝ and n∈ℕ such that n≥2 where ℕ is the set of natural…

Q: a Prove that < 16 – a| for each a, b e R. - V62 + 1 Va? + 1

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Q: =[12] and U- = -[] Then A2017U is equal to -1 Let A =

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Q: 49. Prove that x +> 2 (x1/2 – x-1/2)2. 2 for all x > 0. Hint: Consider

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Q: coprime

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Q: -1 (4) y= coth¯x =- In(²+1, 2 x-1 Prove that

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

A: Given x is a real number such that x≠0 To prove x2&gt;0

Q: Let f(2) = In[="(= + 7)*(z² + 7)°] f'(x) =

A: Given : fx = lnx8x+72x2+76

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: Prove by direct proof: “V n E Z if 2 ł (3n + 5), then 2 | n."

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Q: 2. Let a € R and n € Z0. Show that of the numbers a, 2a, distance from an integer is at most 1/n.…

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: III. Prove the following using Indirect Proof. 13. If 8 ł x in x? + 2x +1 = 3x? – 3x – 9, then x is…

A: The contradiction method comes under the method of proving a statement by the indirect method. In…

Q: R is the amount of rain, in inches, on any particular day in 2012, and it is said to be uniform…

A: Wr want to find the probability by chebycheves inequality.

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

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Q: Using the Mean Value Theorem, we can prove that a. 2* > 1+ xln2 for all x > 0 b. 2* 0 c. 2* =…

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Q: the interval [a, b], where c; is any point in the ith s Interval [-3, 3]

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Q: A. If X~N(196,20), find x such that Pr(X < x) = 0.945.

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

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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: 4. Let R be the set of all real numbers, xER and n EN such that n 2 2. If (1+x) > 0, prove that Pn:…

A: Let ℝ be the set of real numbers, x∈ℝ and n∈ℕ such that n≥2. If 1+x&gt;0, we want to prove that  Pn…

Q: Show that if x ~ Nm (u, 2), where N is positive definite, then (x – u)'N-I (x – µ) ~ Xm: 2

A: Given  x~Nmμ,Ω, where Ω is positive definite.

Q: Prove that P(Ø) = 0. Hint: Let A, = Ø for all i in equation (1.3.3).

A: Consider that

Q: 3. Amit's friend group has n people including him, wheren is a positive number. Prove that at least…

A: Let Amit's friend group has n people including him and their heights are x1 , x2 , ... , xn…

Q: Let x be defined as x = x² -x + 1 for all values of x. If p = p -3, what is the value of p? A 1 BO…

A:

Q: Find all the values of x in the interval [0,2pi], that satisfy the question.  10cos(x)+5sin(2x)=0

A: Given equation is Solve the given equation for x

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

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Q: - Prove thas the scries 2+x2 3+X2 4+x niformcy conuergen2 in any interval?

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Q: Suppose that X~ N(100, 20). For some valle x, we have that P(X ≤ x) = 0.7605. What must be the value…

A: given data x~N (100,20)here μ = 100σ=20p(X≤x)= 0.7605we have to find out the value of x for given…

Q: Q 4. (a). Show that limit *1, does not exist if (5-4x S(x)=. -)- {ax-2 for x <1] for xz1]

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Q: Hallar a de modo que h sea continua para todo ax²-x, x≤-1 ax - 5, x>-1 h(x) =m Envie sus comput X…

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Q: Prove thot if yef(x) is continyous and f(x) =0 when x is a ratsonal number, then f(x) =0 for all x €…

A: Given that y = f(x) is continuous and f(x) = 0, x is a rational number. To prove f(x) = 0 for all…

Q: Let A = 3 21 then A-1 Does not exist O None of these equal to the above Dequal to the above

A: If determinent of metrix is zero then then matrix has no inverse

Q: let n be a positive integer not exceeding 20. How many values of n such that the equation x^2 +…

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Q: Prove that the statements below are true using vacuous proof or trivial proof: a) if 0 24

A: We have to prove that following Statement.

Q: Two runners start a race at the same time and finish in a tie.Prove that at some time during the…

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Q: Prove Bernouilli’s Inequality which states: If x ≥ −2 then (2+ x)n ≥ 1 + nx for all natural numbers…

A:

Q: 3 We can de fine the fallaing tunction on real mumbers ( called "absohite value") ; abs (x) = x if…

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Q: 2. Let A be non singular. Show that if Ax = 0, then x = 0.

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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: If f(x)=x^3/3 -3x Show that f(x) satisfies the hypothesis of the Roll's Theorem on the interval [-3,…

A: Topic:- rolls theorem

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: Find all integer x satisfying the condition x gcd(4x +3, 2x). Justify your answer. %3D

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

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Q: Determine the ratio and interval of con (-1)"x" in=0 n6" O R.O.C=6, 1.0.C: x E [-6, 6) R.O.C=1,…

A: Here we have ∑n=0∞(-1)nxnn6n=∑n=0∞an ⇒an=(-1)nxnn6n