(b) Consider the following set of real numbers: 3n² +n +3 A-3+N} CR { n³ n = :n Prove that A is bounded. (ii) Prove that inf(A) = 0. Can you replace inf by min? Justify your answer. (iii) Find sup(A) and max(A), justifying your answer in each case. [4] [4] [3]

Q: Suppose that |a − 6| ≤ 2 and |b| ≤ 3. (a) What is the largest possible value of |a + b|? (b) What is…

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Q: 8 Find all zeros. a) f(r) = 23 + 3r? – 4x – 12 b) f(r) = a – 7x4 + 10r3 + 14r² – 24x c) f(r) = r(r –…

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Q: Let n(B) = 5 and n(AUB) = 7. (a) What are the possible values of n(A)? (b) If n(An B) = 0, what are…

A: Let A and B be two sets , then  n(A∪B)=n(A)+n(B)-n(A∩B) . Given that n(B)=5 and n(A∪B)=7 .

Q: Consider the following. f(x) = x4 − x3 − 12x2   b) Determine whether the multiplicity of each zero…

A: f(x)=x4-x3-12x2

Q: Transformation of ₂F, : X A x If |x| < 1 and < 1; then: 2³₁ (a, b; c; x) = (1 − x)" ₂ F₁ (a.c-b;…

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Q: Suppose that the functions S and t are defined for all real numbers X as follows. s(x)=x² t(x)=3x³…

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Q: Find the smallest positive integer in the given set. (a) {6u + 15v : u, v ∈Z}    (b) {12r + 17s : r,…

A: Given: (a) { 6u+15v:u,v∈Z }(b) { 12r+17s:r,s∈Z }

Q: LET b₂= SHOW THAT faxi) - faxo). (x₂-xo) f (x₂) - fcxo)_ _faxi) - faxo) (x₂-x₁) (x₂-x₁) (X₁-Xo)…

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Q: Which of the following quadratic polynomials are irreducible? To check, complete the square if…

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Q: Which of the following expressions is NOT equivalent 36 ? to x

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Q: - Let f(x) = -1+x + 2x² – 2x³ – x* + x5. Which of the following statements is true?

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Q: Using the recursive relation I (r + 1) = r[ (r) and the fact that I ย relat 1 2 }} 5 {} and (b) £ =…

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Q: a -1 x² + 2x+- a-5 ; x 0 Find all possible real values of a such that f(x) possesses the smallest…

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Q: Indicate the least integer n for which (3x6 + 2x2)(x3 + 3x) is O(xn).

A: Solution:-

Q: ndicate the least integer n for which (3x5 + x2)4 is O(xn).

A: Solved using the binomial theorem

Q: Find the Domain of f-1, if f(x) = 2(x – 7)² Domain: y is all real numbers Domain: x > 0 Domain: y >…

A: The range of a function f(x) is the domain of the inverse function f-1(x). The domain of f(x) is the…

Q: Find the general solution of the recursive relation an = 2 an-1 - 6 an-2 for every integer n > 1. a,…

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Q: Let P(x) denote the statement "x < 4." P(4) is A) True False

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Q: Show that the first statement is true while the second statement is false. There exist real numbers…

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Q: says this part is wrong Find all other zeros of P(x). (Enter your answers as a comma-separated list.…

A: In this question, we will find the other zeros of P(x).

Q: (a)  Evaluate S(3, 1, −2). (b) Evaluate S(S(3, 1, −2)). (c) Evaluate S(2a, 3a + b, b − 2a), where…

A: S(3,1,-2) A=3-4-21250118 Now, S(v)=Av ⇒S(3,1,-2)=31-23-4-21250118=10-32-17

Q: Consider the set S = {x² + 1, 2x – 2, – x² + x}. The set S spans P2. If t(x) 2x? – 13x + 9 € P2 ,…

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Q: Find the general solution of the recursive relation an = 2an-1-12an-2 for every integer n > 1. None…

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Q: Express the interval shown on the number line in interval notation. -12 -10 -8 -6 -4 -2 0 2 4 6 8 10…

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