1. Prove that the following functions are quasi-concave: (i) f(x, y) = ryt, r > 0, y > 0; e-24, x > 0. (ii) f(x, y) =

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Q: [Groups and Symmetries] How do you solve Q5, thanks

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Q: Given f(t)= 10sin (0.25rt), what is the z- transform of f(t)? z10sin (0.25rt) z-2zcos (0.25nt)+1 zsi...

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Q: (b) Sketch the graph of a function that has a local maximum at 3 and is continuous but not different...

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Q: Let S2 = {a = (a1,a2,a3) E R3 | a1a2 + 2a3 = 0} If y = (y1.y2.y3) E S2 and z = (z1,Z2,z3) E S2, is y...

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Q: Evaluate the following integral by appropriate method: L 12+ |x] dx dx Jyz xVx2-1 L, 12x – 1| dx

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Q: Find the area of the shaded region. y 4 y= 1F1, 1) X = 27

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Q: f (x, y) of a smooth real-valued function f defined on a bounded Consider the graph z subset D of R²...

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Q: 1 Find equations in vector and rectangular form for the a) osculating plane, b) normal plane, and c)...

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Q: Use the formula to compute In(1.11) correct to five decimal places. In(1 - x) = - n-1 In(1.11) =

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Q: The differential equation (x +3y²)y'-y 0 is a first order linear differential equation in standard f...

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Q: IfT: R? → R³ is a linear transformation such that 13 16 (:) - T 26 and T then the standard matrix of...

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Q: 1. Suppose that a group of illegal counterfeiters print 1,000 copies of fake $20 bills and introduce...

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Q: c roots of 2 characteristic root

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Q: n=1 ) Let a, = In(2n +1) – In(2n – 1). Does {an}1 converge or diverge? ) Let SN be the Nth partial s...

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Q: ) Given Xn+1 = X + 2x + 3X, shown below (also shown is Xn+1 = Xn), and X5 = 0.1, what is AX,? a) 0.2...

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Q: ) Given Xp+) = X +2x+ 3X, shown below (also shown is Xn+1 = Xn), and Xs = 0.1, %3D what is AX;? a) 0...

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Q: Show that ø is injective but has no left-inverse, i.e there does not exist a homomorphism ý : S3 → Z...

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Q: Prove the following by using: a contradiction argument; the definition of a logarithm; the definitio...

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Q: Indicate the intervals on which the function f is increasing or decreasing and classify any extrema....

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Q: Using the interval bisection method find the positive root of x – 3 = 0 correct to 4 d.p, with start...

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Q: 2. Consider the series E (In(2n + 1) – In(2n – 1)) . n=1

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Q: 1. A curve passes through the points (1, 0.2), (2, 0.7), (3, 1), (4, 1.3), (5, 1.5), (6, 1.7), (7, 1...

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Q: Finally, we are going to practice the last step. Solving a differential equation using the Laplace t...

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Q: The gradient of a function f is given by Vf = (3x² + 3y, – 3y? + 3x). IS (a) The Hessian matrix of f...

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Q: What is the shortest distance from the surface xy+3x+z^2=12 to the origin?

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