2. Let R be a U.F.D. and f (x), g (x) e R [x]. If f(x) g (x) is a primitive polynomial, then f (x) and g (x) are also primitive polynomials.

Q: 25. y = x² sin“ x + x -2 = x* sin' x + x cos

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Q: Write the first five terms of the sequence, give the exact answer: n n +1 [ n=1 Determine whether th...

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Q: Analyze and sketch the following curves. Indicate critical points and label your graph. I. 1. y = 1/...

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Q: dx 5.

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question s...

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Q: 1. In this problem you will prove that the shortest distance between two points is a line using the ...

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Q: 4 Q1. Find an approximation to V9 using 4 steps Bisection Algorithm

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Q: Find a, b, c E R such that the polynomial f(x) = x³ + ax? + bx + c is divisible by g1(x) = x + 2 and...

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Q: 1 3) For which a does converge? Justify your answer. n(ln n)a n=2

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Q: Consider the function h(x,y,z) = e10-xy + sin(2nz). (a) (i) Calculate the gradient of h. Hence, dete...

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Q: I. Solve the determinant using the Co-factor expansion. (5 pts each) 3. D = -3 3 21 1 4 4. E = 1 I-5...

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Q: Calculate the maturity value of a simple interest, 8-month loan of P7000 if the interest rate is 8.7...

A: Concept: Here we shall use the formula for simple interest, SI=P×r×t100 Here, P is the principal, r ...

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Q: Using the substitution y = vx and dy = v dx+ x dv, the differential equation with homogeneous coeffi...

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Q: Calculate for one real root of tan a = 4æ with ao = 1.2 up to four decimal places using the Newton-R...

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Q: Q.1. Justify why the level curves very close to the origin (0, 0) for the function f(r, y) = (1-)(1-...

A: To find the level curves, equate the function fx,y with a constant C.

Q: Nhat is the equation of the family of parabolas with vertex and focus on the y-axis? A (y-k)² = ± 4a...

A: A parabola is an equation of curve in which a point on the curve is equidistant from a fixed point a...

Q: Use Green's Theorem to calculate the line integral shown in the figure, along the C curve that consi...

A: Given integral is ∫Cxydx+2x2dy. We have to calculate the given line integral along the C curve that ...

Q: In integrating the function fx cos(3x) dx using integration by parts, what would be your du? du = x ...

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Q: By using Laplace transform to solve y" – y – 2y = 4 with y (0) = 1 and y (0) = 4 , what would the pa...

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Q: In each graph, a parent function has undergone a transformation of the form f(kx). Determine the equ...

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Q: hat are the roots in the given polynomi 10

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Q: Using Fixed-Point Iteration with an initial value of 4, HOW MANY NUMBER OF ITERATIONS are needed to ...

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Q: Find the eigenvalues and corresponding eigenvectors for the matrix 8. -8 -2 A = 4 -3 -2 3 -4 1 Write...

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Q: max Z = x1 + 3x2 + 5x3 4.x1 + 3x2 + 6x3 0 Say we use x4, X5 as slack variables for the first and se...

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Q: In a concert hall, the ceiling can be described by the plane x + y + z = 30. An audio engineer is tr...

A: Lagrange multiplier method: If f(x, y, z) is a function such that g(x, y, z)=0 then optimal values o...

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Q: Solve (x² + 4)y' = 2xy In|x] = In(y? + 4) +C O Option 1 Inlyl = In(x² + 4) +C

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Q: Describe the image of the real x-axis in the uv-plane under f(z) = iz + z

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Q: Use Laplace Transforms to solve the IVP 3y" + 6y/ + 3y = 9, y(0) = 0, y (0) = 6 %3D

A: We need to use laplace transformation table for  L(y''(t)=s2Y (s) − s y(0) − y'(0) L(y(s))=  sY (s) ...

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Q: 1. Evalute the improper integral 3x dx. J ' 1+ x² -1

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

Q: Use forward-difference formula to evaluate the first derivative of y = x² + 4x – 5 at a = 0 using a ...

A: The forward difference formula is : f'(x)=f(x+h)-f(x)hWe have to find the first derivative of y=x2+4...

Q: Use Green's Theorem to calculate the line integral shown in the figure, along the C curve that consi...

A: We have to evaluate ∫Cxydx+2x2dy by using Greens theorem along the curve C that consists of the line...

Q: Problem 7. Consider the matrix 1 1 a A := 1 b b C C C Find all possible combinations of values a, b,...

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Q: Consider the function f(x) = x³. Construct the Lagrange interpolation polynomial which interpolates ...

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Q: The general solution of the DE: In-2y dx – y-le-*dy=0 is A None of the given choices В 3e3* – In³y=c...

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Q: The volume of a solid bounded by surfaces: z= 0,z=Vx? +y?,x²+y² =1

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Q: Let S = {(1,1), (1, 2), (2, 1), (3, 2), (3,3)}. Consider the polytope conv(S). Write this set as {r ...

A: The given set is S=1,1,1,2,2,1,3,2,3,3. We know that the polytope:  ConvS=λ11,1+λ21,2+λ32,1+λ43,2+λ5...

Q: Converges, its sui Enter the exact answer as an improper fraction if necessary. If the series diverg...

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Q: ors to be exactly 7:1. Use the table below to organize the given

A: given the following information  unit given rate unknown rate campers 7   counselors 1   to...