Find all relative extrema of the function. Use the second derivative test where applicable. (If an answer does not exist, enter DNE.) f(x) = x8/9-7 relative maximum (x, y) = relative minimum (x, y) = Need Help? Read It DNE Watch It ✓ X ) )

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Q: Answer true or false for each of the following questions and give justification for your response.…

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A: Let F be a field and let f(x) be a polynomial in F[x] that is reducible over F.

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Q: (d) Bi 100 i=1

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Q: 2. Given: f(x) = I (x - 1)² - - x, with f'(x) = -x(x²-3x+4) (x - 1)³ and f"(x) = - 2x: +4 (x - 1)¹…

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Q: Consider the polynomial P(x) = 4x6 - 4x5 + 11x¹ - 7x³ +5x² + 2x (a) Use the Rational Root Theorem to…

A: Rational Root Theorem:- A rational root of a polynomial  Px = an xn + an-1 xn-1+……+a0 is of the form…

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Q: lim sin z

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Q: (a) lim (x,y)→(1,−1) 2x + y - 1 x² — y² + 1

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Q: Question 2) Let L={ a¹ b³ | i, j≥0 and i>j }. Is L regular? Prove your answer. Show all your work.

A: Let a is replaced as 0 and b is replaced as 1.

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A: The total volume is 450 cm3 We know for a rectangular box, volume = length×breadth×height

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Q: 8. Shade the sets с (with B B (Anc)n B and (ANC)UB.

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Q: 1 2. Prove that for r < 1, we have the following inequality: e* < I

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Q: (a) VA: VB: (VC: AUC = BUC) → (A = B) (b) A: VB: (C: AUC = BUC) → (A = B) (c) A: VB: (VC: ANC = BNC)…

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Q: Set V₁ = 1 V2 = 2 V3 = D----| 3 B = {V₁, V2, V3} is a basis for R³ (you don't have to verify this).…

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Q: Any proper subgroup S of a nilpotent group G is proper subgroup of its normalizer in G.

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Q: Consider the polynomial P(x) = 4x6 − 4x5 + 11x4 7x³ +5x² + 2x - 2. (d) If (√2)i is a complex root of…

A: Given polynomial is                               P(x)=4x6-4x5+11x4-7x3+5x2+2x-2     Given  2i is a…