(i) Find the infimum and supremum in each of the following sets of real numbers: S = {r| – x² + 6x - 3 > 0

Q: Let S = {x² : |æ| < 0}. Find each of the following values. For the infimum and supremum, your answer…

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Q: Show that there is a root of the equation x3 - x - 1 = 0 between 1 and 2.

A: Consider the given equation. x3-x-1=0 and, fx=x3-x-1 Put x=1 in the function. f1=13-1-1=-1

Q: determine k such kx2 - 4x +1/2 = 0 that has real and different solutions

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Q: Find two positive real numbers x and y such that their product is 800 and x + 2y is as small as…

A: Given that, We have to minimize:

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Q: Find two positive real numbers x and y such that they add to 120and x 2y is as large as possible.

A: Given: x+y=120and  y=120-xAlso given that z=x2ybut we have z=x2120-x=120x2-x3    ...(1)

Q: Give a possible formula of minimum degree for the polynomial h(x) displayed in the graph to the…

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Q: The positive value of k for which x2 +kx+64=0 & x2 -8x+k=0 will have real roots

A: Given the quadartic equations(1)x2+kx+64=0(2)x2−8x+k=0

Q: と 2 2. X: X.. に こ1 provethate

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Q: (c) Prove that the equation x + 5x = 4cos.x cannot have more than one real root.

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Q: The positive value of k for which x2+kx+64=0 & x2-8x+k=0 will have real roots

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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: 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: 3. Find the infimum and supremum, if they exist, of each of the following sets: A = {x € R: 2x + 5 >…

A: see 2nd  step

Q: 14. The condition for the quadratic cquation x2 + 2kx + (k + 6) = 0 to have two uncqual real roots…

A: When a quadratic equation have two real unequal real roots then the value of discriminate is greater…

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

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Q: 0=1+xx + ₂X4₁

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Q: Find the zeros and give the multiplicity. f(x) = x2(4x + 5)°(x - 6)2 X = (smallest x-value) with…

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Q: 4) a) Show that the equation y = x³ + 3x2 + 16 has exactly one real root. What is it

A: To show That the equation y=x^3+3x^2+16 has exactly one real root.

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Q: Find the Domain of 1, if f(=) 0(s-6) %3D O Domain: y is all real numbers O Domain: y N0 O Domain: NO…

A: Given f(x)=6(x-6)2 To find f-1, assume y=f(x) then swap variables to find f-1

Q: (b) Expand and simplify in ascending powers of x as far as the term in x" 1+3x

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Q: Q1) A: Proof that <- where x & y E to the rational numbers. B: Solve the following inequalities and…

A: 1(A) prove that 1x&lt;1y where x,y∈ℚ solution we have 1x&lt;1y that is 1x-1y&lt;0⇒y-xxy&lt;0 as we…

Q: 1 Determine k such kx -4x+==0 that has real and different solutions.

A: A quadratic equation ax2+bx+c=0 has real and different solution if b2-4ac&gt;0

Q: O INTENATUNAL SCHUUL Find the condition for 2x² +3kx + 4c to be positive for all real values of .

A: To find the condition for 2x2+3kx+4c  to be positive for all real values of x.

Q: If lim 12 00 k-1 (-1)*k 3x +4x +5 lim T-00 ar + 6x +7 34 then what is the value of the real number a…

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Q: (a) Prove that the equation has at least one real root.(b) Use your calculator to find an interval…

A: Given equation:x5-x2+2x+3=0(a) We have to prove that the equation has atleast one real root.(b) By…

Q: Find the supremum and infimum of the set {x € R|10/T – I > 0}, if they exist. If they exist, provide…

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Q: 2 Find the limit infimum and supremum of 2 XA = √√√ 1+n² √1tn 2A-5 write the complete solution.

A: Limit infimum and limit suprimum

Q: (-1)" n (k) {n+ (m) {r E Q : r² < 4} (0) {x E R: x < 0} :n e N} n

A: Note: Our guidelines we are supposed to answer only three subpart . Kindly repost other subpart as…

Q: 8. Find all the roots of f(x) = x' - 4x' +6x² – 4x+5 if 2– i is one root.

A: We will find all the remaining roots as following.

Q: A real root of x3 – 3x? + x +7=0 lies between two consecutive integers. Find these two integers.…

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Q: 1. Use the Intermediate Value Theorem to show that there exists at least one solution in the set of…

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Q: 5) Find all real solutions: x -6x% =-1

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Q: (2) Determine k such that kx – 4x+=0 has real and different solutions. 2

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Q: Solve the following rational inequality for x. Give your answer in interval notation. Provide your…

A: Let's solve for x.

Q: All the real roots of a polynomial p(x) of degree nine are listed below. The multiplicity of each…

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Q: If f(x) = 3x2 + βx + 4 and f(−1) = 12, what is the value of β? 2)     Show that If 2 is a root of…

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Q: The positive value of k for which x2+kx+64=0 & x2-8x+k=0 will have real roots

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Q: -2 Find all the values of s €R such that A = -2 -2 is positive definite.

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Q: と 2. X.. Q3 「ニ」 Prove thete

A: We have to proof the given statement

Q: 9. Find all real zeroes of the function p(x)=6x' +17x² – 26x +8

A: Definition used-              Rational zero theorem  -                       If a…

Q: use the discriminant to help solve each problem. Determine k so that 4x2 - kx + 1 = 0 has two equal…

A: For a quadratic equation ax2+bx+c=0 the discriminant can be used to determine the number of real…

Q: For all real numbers x, what is the maximum value of 5 sin 2x? A. 1 BO 10 2(pi)/5

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Q: Prove that the equation x- 15x +k = 0 has at most one root in the interval [-2, 2]. Hint: You'll…

A: Dear friend,  if you have any other query about this problem, then please tell me about your query I…

Q: Find the value of k in the equation x2 – 3x + k = 0 if its roots are real, irrational and not equal.

A: Since you have multiple questions in a single request. we would be answeringonly the first question…

Q: Find a real root of 4*exp(-x/2)-3*In(x)-3 = 0 using False Position method with a=0.1 and b=2.0…

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Q: Q1: Prove that the equation x2 = 7 has a unique positive real root. %3D

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Q: Solve for x. (Enter your answers as a comma-separated list.) In(x) + In(x + 8) = 0 X =

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Q: Find the number in {x E R:-2<x<2} such that the sum of that number and its square is a maximum.…

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