Question 1 a. Evaluate. i. ii. i lim X0 (-81+(x-9)21 (16-x2) lim X→-4 16+4x/ lim x→0 3-Vx²+9 2

Q: Evaluate the following integral (use Integration by Parts) Su².. sin³u-5 1-cos²u du

A: Solving integration by parts

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A: Please see the attachment

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A: Follow the steps.

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A: We shall solve first question only as you have asked more them one different question. For others…

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A: Given function is f(x)=x3+2x2-11x-12 Graph of the function is Since the graph cut the x-axis at -4,…

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A: Second statement is true  in Z.

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Q: 20. Determine the eigen values of the following matrix: 5 15 31 21 a. 1, 6 b. 4, 1 c. 3, 4 d. 2, 5

A: The solution is given as

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A: 1. (a) Given,               Max Z=3x1+6x2subject to       3x1+4x2≥12    -2x1+x2≤4and      x1, x2≥0

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Q: Part II. Direction: Solve for the root and the iteration function g(x) of the following functions…

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Q: Max 3A + 2B IA+IB ≤ 10 3A +1B ≤ 24 1A + 2B ≤ 16 A, B 0

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A: Follow the steps.

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A: We have to solve given problems:

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Q: 5. Solve for one value of x in x cubed - 8 = 0. a. 1 + 1 sqrt of 3 b. -3 c. -2 d. -1 - sqrt of 3

A: To find- Solve for one value of x in x3 - 8 = 0 1 + i3 -3 -2 -1 - 3   Formula Used-  a3 - b3 = a…

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Q: (ii) Use Stokes' Theorem to evaluate F. dr, where F(x, y, z) = x²zi+xy²j+z²k and C is the curve of…

A: Given function F(x,y,z)=x2z i^+xy2 j^ +z2k^  Plane: x+y+z=1 Cylinder: x2+y2=9

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A: Solution is given below:

Q: 1] Let x,yER. Prove that VxVy(4x+9y>9⇒(x>5/4 Vy> 4/9)) using method of indirect proof. 21 Let x VFR…

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

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A: Given: μ=69.0, σ=2.8, and z-score=0.5 To find: Height of man with given z-score.

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A: To evaluate measure of angle of an arc

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Q: Prove that for all natural number n, 52n-1 is divisible by 8.

A: Will prove the result by mathematical induction

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Q: Max 3A + 2B S.I. IA+IB ≤ 10 3A+IB ≤ 24 IA + 2B ≤ 16 A, B≥ 0

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Q: 2) Consider a horizontal parabola of the form ay² +by+c = x where a ‡ 0, and whose graph contains…

A: Given the horizontal parabola of the form ay2+by+c =x and the graph contains the point (-1,3),…

Q: 4. y(y² - 2x²) dx + x(2y² - x²)dy = 0 [Answer: x²y² (y² - x²) = = C

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Q: ) Consider a horizontal parabola of the form ay² + by + c = x where a ‡ 0, and whose graph contains…

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Q: Use your knowledge of the Rational Roots Theorem to find the zeros of f(x)=x²-3x² - 10x + 24. Then,…

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