3. Express using absolute value notation. a) x<-3 or x> 3 b) -8 < xs8 c) xs-1or x21 d) x + ±5

Q: express the set of numbers x satisfying the given condition as an interval.       I x+ 7 I &lt; 2

A: Given: x+7&lt;2 We know that solution of inequalityx+a&lt;b is given by -b&lt;x+a&lt;b

Q: Use interval notation to represent all values of x satisfying the given condition. y = 7 -  | x/2 +…

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Q: Use interval notation to represent all values of x satisfying the given conditions: y = 1 - (x + 3)…

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Q: If x, y and z are three real numbers such that x+ y+ z= 4 and x + y + z = 6, then show that each of…

A: Introduction :

Q: 4 z+9 (z – 2) + 2 (9 – 2) < 18 (x + 1) Enter the exact answer in interval notation. -To enter 00,…

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Q: Prove that the Intermediate Value Theorem remains true when the inequality sign is flipped, i.e.…

A: We know that According to Intermediate Value Theorem: A function is continuous in interval  I = [a ,…

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: Find the domain of f(x)=x² for 0<x<5. O (1,25] O (0,25) O [0,25] O [1,25)

A: Given: The function is fx=x2 for 0≤x≤5. To find: The domain of the given function. The given options…

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A: Here given function  fx=3x4+2x2 it is a polynomial function thus it is continuous on [-2, 2] and…

Q: Use Definition 1.1.4 to prove that {x:|x| 0, and -x if x < 0.

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Q: Show that the interval [a,b] is complete

A: Given

Q: Prove or disprove: If x and y are real numbers with y 2 0 and y(y + 1) < (x + 1)², then y(y – 1) <…

A: We have to prove or disprove that if x and y are real numbers with y≥0 and yy+1≤x+12 ,then yy-1≤x2.…

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A: Archimedian property : For every positive real number c there exist a natural number n such that…

Q: Let x and y be postive numbers such that x+2y=50. Fing the values of x and y that make the quantity…

A: Here we will use the concept of maxima and minima to solve this question

Q: Q3/ By using definition, proof that cot x = - csc² x. xp

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Q: 4. Use the definition of "f(x) is 0(g(x))" to show that 2* + 17 is O(3*).

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Q: Ifx and y are positive real numbers, use the direct method to prove the following inequality: Vxy s*…

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Q: 62. Let D be the domain bounded by y = x2 +1 and y = 2. Prove the incquality 4 20 (x² dA 3

A: The domain is y=x2+1 and y=2. Sketch the domain D as shown below.

Q: express the set of numbers x satisfying the given condition as an interval.          I 4x - 1 I ≤ 8

A: 4x-1≤8

Q: Show that the equality [r + y] = [2] + [y] is not valid for all real numbers r and y.

A: Consider the provided question, We first define ceiling function. The ceiling function maps x to the…

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Q: Use Proof by Cases:  If ∀ (x,y) ∈ ℝ^2 (x and y are real numbers), then | |x| - |y| | ≤ |x - y|

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Q: o Yes, zero is contained in the interval.

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Q: Use interval notation to represent all values of x satisfying the given conditions: y = 2x - 11 +…

A: It is given that,y = 2x - 11 + 3(x + 2) and y is at most 0. We have to use interval notation to…

Q: express the set of numbers x satisfying the given condition as an interval.       I 3x + 5 I &lt; 1

A: To solve the inequality: 3x+5&lt;1 Solution: We know that if x&lt;a then -a&lt;x&lt;a. We have…

Q: If f(x) = -7e*, th %3D

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Q: Express the set of real numbers between but not including 2and 7 as follows.(b) In interval…

A: given: 2&lt;x&lt;7 given expression in interval notation can be written as below x∈2,7

Q: Prove the inequality √1+x≤1+x2 for x&gt;1.

A: Consider the function. Find its derivative.

Q: In interval notation, [2, 5) represents the set of real numbers between______ and_______ ,…

A: The given statement is, In interval notation, [2, 5) represents the set of real numbers…

Q: The interval notation for the set (xlx ≤4 or x>-2} is. [-2,4] A O (-2,4] BO R .CO DO [-2,4) EO…

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Q: Hi I have attached the question. Thanks

A: To prove that the complex number z is real under the given conditions

Q: Let x be a real number. Prove by contrapositive that if x + 5x = 40, then x < 3.

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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: 6. Prove that |x.y| = |x|.|y|, where x and y are real numbers.

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Q: The Intermediate Value Theorem can be used to prove that the equation x2 – x – 6 = 0 has at least…

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Q: O Prove that V5 is irrational. (ie. explain why complete

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Q: In interval notation, [2, 5) represents the set of real numbers between and including but not…

A: Given that: In interval notation, [ 2, 5) represents the set of real numbers between  _________ and…

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

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Q: Prove or disprove: If x and y are real numbers with y ≥ 0 and                           y( y + 1) ≤…

A: Given equations - yy+1 ≤ x+12             ....................(1)yy-1 ≤ x2…

Q: Prove the implication: For all real numbers x and y if x + 2y > 42, then x> 21 or y > 10.5.

A: The solution are next step

Q: The Intermediate Value Theorem can be used to prove that the equation 2²-2-15-0 has at least one…

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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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Q: 1 -Find all the points where f(2)is analytic. 2+3 Let /(2) =

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Q: 32 (c) Show that Hence, find the interval for x that satisfies the inequality = 22* 2 x 4" 32" -…

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Q: 1 1 2 x y x+y || +

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