C and D are sets of real numbers defined as follows. C={z|zs1} D={z |z<9} Write CUD and Cn D using interval notation. If the set is empty, write Ø. (0,0) [0,0) ) (0,0) CUD =| [0,0) CND = Ø -00 8.

Q: Find two positive real numbers x and y such that they add to 120 and x2y is as large as possible.

A: Oue Aim is to find two positive real nnumbe x and y such that theyadd to 120 and x2y is as large as…

Q: C and D are sets of real numbers defined as follows. C={z | z>1} D={z |z>8} Write CUD and Cn D using…

A: Given are the sets as follows: C=z|z≥1D=z|z&gt;8. Here z∈ℝ. It is required to find C∪D and C∩D. The…

Q: Determine the positive real numbers x and y such that • x + y = 4 and 2.n2 + y² is small as…

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Q: Which of the following is always true for any real numbers x, y? For real ɛ > 0, if |x-y| 0. m >n…

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Q: F and H are sets of real numbers defined as follows. F={v|v< 4} H={v]vs6} Write FO H and FUHusing…

A: F and H are sets of real numbersF=v|v&lt;4H=v|v≤6

Q: Determine the interval(s) on which x2 + 2x – 3 > 0. - Ох1 Ox 1 -3 1

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Q: (2) The floor function is defined as a| = max{m e Z|m < x}. Effectively, the floor function is the…

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Q: Let R; = {x E R|15 xs 1+ = 1, 1 + for each positive integer i. (Enter your answers using interval…

A: Hey, since there are multiple questions posted, we will answer the first question. If you want any…

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: Suppose that the functions r and s are defined for all real numbers x as follows. r(x) =x-4 s(x) =…

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Q: Let R, - {r E R|1 5 x3 x < 1 for each positive integer i. (Enter your answers using interval…

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Q: The domain of h(x) 7 - consists of all real numbers except 0 and 3, represented in interval notation…

A: Given function is hx=1x+7x-3. To find domain. Solution: Domain of a function is the value of x for…

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: Find the supremum and infimum of the set x € R:x = +(-1)" ,n e N} + (-1)" ,n e N}

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Q: If x and y are real numbers and x>1, prove that there exists a positive integer n such that xn > y

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Q: 1 1. LET A= [x € r: x + 2] and B= [y € r: + ?]where r is the set of real numbers. given that f: A →…

A: Givenfx=x1-2x

Q: B and C are sets of real numbers defined as follows. B = {w | w>1} C = {w | w<9} Write BUC and B n C…

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Q: Consider the set S = {r E Q : r² < 2}. In the land of rationale numbers is there a least upper bound…

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Q: Suppose that the functionss and t are defined for all real numbers x as follows. s (x) = x t (x) =…

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Q: 1. The set of all pairs of real numbers of the form (x, 0) with the standard operations on R2.

A: 4. Given that the set of all pairs of real numbers of the form (x, 0) with the standard operation on…

Q: F and H are sets of real numbers defined as follows. F={v|v<4} H={v]v<6} Write Fn H and FUHusing…

A: F = v|v&lt;4H = v|v≤6F∩H = those element/numbers continued in both F and H

Q: If an inflection point of the aurve f(x)=acos(2x) +bsin(3x) is P(n /6,5), then what are the real…

A: The given function is fx=acos2x+bsin3x. Substitute the point x, y=π6, 5 in fx=acos2x+bsin3x.…

Q: D and E are sets of real numbers defined as follows. D= {v|v> 1} E= {v]vs 8} Write Dn E and DUE…

A: Given D = { V | V &gt; | }           E  = { V | V ≤ 8 }We find D ∩ E and Due using interval nolation…

Q: Letx, y, and z be positive real numbers. Show that: xyz(x+ y+z)sr°y+ y°z+z°x

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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: Suppose that the manufacturer of a gas clothes dryer has found that when the unit price is p…

A: topic - functions

Q: Let a1, a2, ...,a, be real numbers that are all contained in the interval [-7/2, 7/2]. Use the…

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Q: Suppose that the functions r and s are defined for all real numbers x as follows. r(x) = 6x s (x) =…

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Q: Find functions f and g from the set of positive integers to the set of real numbers such that f (n)…

A: Here, we need to find functions f and g from the set of positive integers to the set of real numbers…

Q: Z is the set of integers, R is the set of real numbers. 1. Functions f, g, and h are defined as f:R…

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Q: Z is the set of integers, R is the set of real numbers. 1) Functions f, g, h are defined as f: R ->…

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Q: Suppose x is a real number. Prove that if x 2, then there is a real number y such that x = (2y + 1)/…

A: Domain of a Function The domain of a function explains what values the independent variable, X, can…

Q: Define Floor: R → Z by the formula Floor(x) = for all real numbers x. Here are some example values:…

A: See the proof and counter example below.

Q: E and F are sets of real numbers defined as follows. E={y]y<1} F= {y]y<8} Write E UFand En F using…

A: The given question can be solved as shown in step 2.

Q: The functions h and m are defined on the set R of real numbers by h:x→ ax +b and m:x → cx -d, where…

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Q: (d) Using Part (c) and continuity of g, prove that g(x) = mx + l for some m, l e R.

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

Q: F and H are sets of real numbers defined as follows. F = {w | w< 4} H= {w |w< 5} Write FU H and FN H…

A: Given F and H are sets of real number defined as followsF = W|W&lt;4H = W|W≤5We find F ∪ H and F ∩ H

Q: Suppose that the functions r and s are defined for all real numbers x as follows. r(x) = 6x s (x) =…

A: Given  rx=6xs(x)=2x+3 where the expression for r+sx,  r-sx  and  r·s2 is to be evaluated.

Q: If an inflection point of the aurve f(x)=acos(2.x)+bsin(3x) is P(7/6,5), then what are the real…

A: Given: fx=acos2x+bsin3x; pπ6,5 We know that point P is inflection point of the curve, so it lie on…

Q: 2) Use Rolle's Theorem on f(x) = 2x3 - 6x² - 2x + 6 to find all numbers c in the interval (1, 3) for…

A: Here is the solution:

Q: 5. Find interval values for Z such that P(-z <Z < z) = 0.9886.

A: Given, Pz&lt;Z&lt;z=0.9886and Z~N0,1

Q: If x and y are real numbers and x>1, prove that there exists a positive integer n such that x" > y

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Q: Suppose that the functions r and s are defined for all real numbers x as follows. r (x) = 3x s(x) =…

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

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Q: If an inflection point of the aurve f(x)=acos(2.x) +bsin(3x) is P(z/6,5), then what are the real…

A: At inflection point :   d2dx2fx=0d2dx2acos2x+bsin3x=04acos2x+9bsin3x=0

Q: 5. The set of all pairs of real numbers of the form (x, y), where x ≥ 0, with the standard…

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Q: a) Verify Rolle's Theorem for ƒ(x)= 2.x' – 8.x + 4 over the interval [0,2].

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Q: Let R be the set of real numbers and f:R- (1,00[ and g: R→R be defined as f(x) = x² +1 and g(x) = x…

A: Given:- f:R→1,∞      by f(x)=x2+1g:R→R             by g(x)=x+1 Now, f∘gx=fgx f∘gx=fx+1 f∘gx=x2+1+1…

Q: Let a and y be real numbers. Prove hat, Say>I1, hen>2 ory>L

A: