How can I explain using (x0+ ε, x0-ε)? Explain why it is true that, if x0 is in (a,b), then there must be real numbers in (a,b) that are both smaller than and larger than x0. Why is this not necessarily true for [a,b]?

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: A and Bare open and bounded.

A: For second one we can take any two open interval one of whose right end point ar same of the others…

Q: 4. [5] Please find in interval notation the values of x for which this expression is real. Show…

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Q: dominio de la función m(x)=(x−1)(x+2) / (x+5) is ? Steps please

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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: The sum of two positive real numbers x and y is 6. Find an x and y among these such that the product…

A: We need to find x and y.

Q: Show that x3 +x – 1 has a root in the interval [0,1]. (R

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Q: Let S = {(x, y) : x and y rational numbers}. a. What is the interior of S? Justify your answer by…

A: A point x is said to be an interior point of S if there exists a neighborhood N(x) of x such that…

Q: The sum of two positive real numbers x and y is 3. Find an x and y among these such that the product…

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Q: How can I show that f(x) is O(x2), where f(x) = 6x2 + x + 1

A: Given: f(x) = 6x2 + x + 1

Q: Evaluate x-(xy-y) for x satisfying 4(x+4) = 5x+20 and y satisfying -9y-8=7y+24. x- (xy-y)= (Simplify…

A: We will solve the following

Q: Let A = %3D {x €N|2 < x < 7|} . What is n(A)?

A:

Q: 9. For |x|<1, prove that 8x 16x 24x 1-x1+x 1-x 2 8x 8x = 1+ (1 – x)? (1+x2 (1-x)? ...

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Q: I have to find the domain of f(x)= (sqrt: x + 8)/ x-8 and I understand how to find the domain of a…

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Q: A semi-circle of radius r is centred on the origin and has an inscribed rectangle. Find an…

A: NOTE: Refresh your page if you can't see any equations. .

Q: Solve the infonalnky 2x 5X L8x-20

A: Hi there! Thank you for the question, but as per our guidelines, we can solve only one question at a…

Q: Show that the multiplicity of (x-1) is 1.

A:

Q: For a closed rectangular box, with a square base x by x cm and height h cm, find the dimensions…

A: Given: The volume of rectangular box is: V=18 cm3 The rectangular box can be drawn roughly as:

Q: how would you rewrite 2x^2+x-6 to show the roots (zeros) of the function f(x)=2x^2+x-6

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Q: find the anti- deriva tive of the fun cticn: fcx) = 4 cSca cotx - Secx cot x

A: Derivative of function

Q: The intermediate value theorem can be used to prove that the equation x^2+7x+6=0 has at least one…

A:

Q: 2 If f(x) = x+ 8x + 12 and g(x) = x + 6x + 8 then (2) (Make sure your answer is fully simplified %3D…

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Q: Does the Nearest Point Theorem in R imply that there is a strictly positive real number nearest…

A: The statement of the Nearest Point Theorem is as follows: "Let A be a non-empty closed convex set in…

Q: If f(x) <0 for all real numbers x then f is decreasing or increasing on its interval?

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Q: @[V2]is Principal Ideal Domain. O True O False

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Q: 27 comp 28. 8 comp 29. +9° +90 27 = x2-6x 28 = 3x2 - y 3-x2 - 13x + 9 Find mz8. What is the name of…

A: Complementary Angles:- Two angles are complementary if the sum of the measures of both the angles is…

Q: Show that Rsta is Hausdorff.

A: Note that a topological space X,I is said to be Hausdorff if (and only if) for every distinct points…

Q: 4. Show that the real number VV2 – 2 is algebraic. (Here 2 is a real number that satisfies (2)3 =…

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Q: Comment on the accuracy and applicability of the three rules( Simpson, Trapezoidal, and Mid-ordinate…

A: Numerical integration

Q: Solve the inequality for u: µ – x| < Vn (Do not rationalize the denominato)

A: First we get rid of the absolute sign Subtract mu from each side

Q: Give a proof by cases that [4x] = [x] + [x + ¼ ]+ [x + ½ ] + [x + ¾ ] %3D

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Q: what do you get when you expand x+4/xy^2?

A: We can make it easier for you

Q: The algebraic translation of "x is no more than 7" is

A: the algebraic translation of "x is no more than 7 " is ?

Q: Show that 2Vx < e* for all real numbers x.

A:

Q: evaluate x2 -(xy-y) for x satisfying x/9 -7 = x/2 and satisfying -3y -5=4y+23

A: See the details solution in below

Q: How can you write any real power of x as a power of e? Are there any restrictions on x? How does…

A: According to the given information it is required to write any real power of x as a power of e.So,…

Q: What happens if you take B = 2 π in the addition formulas? Do theresults agree with something you…

A: Since, the addition formulas are given below:-sin (A+B)=sin A cos B +cos A sin B -(1)and cos…

Q: Alice is in a 20-km running race. She always runs the first half at an average speed of 2 km/h…

A: Alice is in a 20-km running race.She always runs the first half at an average speed of 2km/h faster…

Q: What is the domain of { (z,3z2- 5) Iz ER except 0}? All real numbers All negative numbers {x\x€R>0}…

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Q: The function f(x) = 4 for x < 2 and f(x) = 4 for x 2 2 has domain of all the real numbers. To True O…

A: As we know that domain is all the value of input (x-values) for which a function can define. for…

Q: (i) Show that f(x) = 6x³ – 2x2 + 4x – 3 has exactly one real root. (j) Show that f (r) = x + 2x5 +…

A: Given: i. fx=6x3-2x2+4x-3ii. fx=x7+2x5+3x3+14x+1 To Show: Given equation has exactly one real roots.…

Q: Find two positive real numbers x and y such that they add to 123 and  x2y  is as large as possible.…

A: We have to find out x and y

Q: ind the domain and range of the function f(x)=square root of 49-x^2 . Express with interval…

A: Given function is y=49-x2

Q: If x is a n-700 as a. always b. real number Sometimes never such that 1x11, then x" -> -0

A: We want to find correct answer.

Q: The algebraic translation of "x is no less than 7" is .

A: Given statement is "x is no less than 7:. To translate into algebraic form. Solution: Given that x…

Q: x^2 + 1/x^2 > 2

A: Here we use a property of real number which is square of any real number is non negative.

Q: "8 does not divide x^2– 1 if x is even". prove it directly

A: We need to prove  8 does not divide x2 - 1 , if x is even. OR if x is even, the 8 does not divide x2…

Q: For f(x) = 4x + 12x, find the number c in (-4, 1) guaranteed by Rolle's Theorem. %3D (Use symbolic…

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Q: 29. For |x|<1, prove that 16x 24x 8x 1 + 1-x1+x 1-x ..... .. 8x 8x = 1+ (1- x)? (1+x)²' (1-x)?

A: