1. Define f: R → R by f(x) = ar³ + br for a, b = R. (a) For which a, b is f injective? Prove your answer. (b) For which a, b is f surjective? Prove your answer.

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Q: Observe the set Is D bounded/closed/open/compact / convex? D = {(x,y) ERIy2x²-1 and y ≤4-e"}

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Q: (x, y) of the point with polar coordinates What are the Cartesian coordinates (r, 0) = (4, 5 ) ? O…

A: Given (x, y) = 4, π6

Q: Minz = S. to X₁ + 2x₂ 2X1- X₁ + 3 X. 7, Xz

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Q: Consider the polar curves C1 :r = 3 sin 20 and C2 : r = 3 cos 0, and let R be the shaded region as…

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A: see attachments

Q: 3. R: y = x²,y = 2x axis of revolution: x – axis

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Q: find inverse Laplace transforms of {s^-3/2}

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Q: Find a non-zero vector perpendicular to the vectors and ú =

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Q: The particular solution of the following equation by using the D Operator y" +2y' + 3y -2x +3 2 13 2…

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Q: Solve the given differential equation by finding, as in Example 4 of Section 2.4, an appropriate…

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Q: 17. Determine the value of fx dy - y dx, where x(t) = (cos 31, sin 3r), 0 ≤ ≤n.

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Q: Consider the polar curves C1 : r = 3 sin 20 and C2 : r = 3 cos 0, and let R be the shaded region as…

A: The area bounded by two polar curves: r1=fθ1 and r2=fθ2 is defined as A=12∫αβr12-r22dθ, where r1 is…

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A: This is a problem of Numerical Analysis.

Q: 1) Are the following functions analytic? a) f (z) = z z b) f(z) = z + z2

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Q: QUESTION 1 Given the recursively defined sequence: a₁ =2, and a = 3a, The first 5 terms in the…

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A: Given curves C2 : r=4cosθ and C3 : r=4sinθ Cartesian equations C2: x2+y2=4x and C3: x2+y2=4y

Q: Are the following numbers Gaussian primes ? Explain why why not. or (а.) 2 — 5, (b.) z = 5- 4i. tr

A: Gaussian integers and Gaussian primes

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Q: Solve the given differential equation by separation of variables. dy xy + 6y-x-6 = dx xy-7y+x-7

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Q: Use intervals to determine the values of x that satisfy the following inequality: 3x³-25x²-52x + 20>…

A: The given inequality is: 3x3-25x2-52x+20>0 Find the zero of the polynomial px=3x3-25x2-52x+20.…

Q: О 1 A = -4 7 ix? -2 5 -8 3 -6 9

A: Solution