3. In the following problems use the appropriate algebra and the appropriate formula to find the inverse transform of Laplace d) f(s): 5²-6 s(s+1)(s+3)

Q: Write six different iterated triple integrals for the volume of the tetrahedron cut from the first…

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Q: The set B = {4- 2x², 12 + 3x − 6x², 18x² - (35 + 6x)} is a basis for P₂. Find the coordinates of…

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Q: Use a Maclaurin series in this table to obtain the Maclaurin series for the given function. f(x) = x…

A: The given function is .The aim is to find the Maclaurin series for the given function.

Q: 3. Display an argument to show that the Gamma Function is defined for s> 0. T(s) = f e-¹4³-1 dt. 0

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Q: Let F be the vector field F(x, y, z) = xi+yj+5zk and let S be the part of the cone z = √x² + y²…

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Q: Apply the eigenvalue method to find a general solution to the system: x' = 4x+y+4z y' = x+7y+z z' =…

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Q: (a) Number (b) Number (c) Number i i Units Units Units < <

A: i) Change in momentum/second=m=5*10-3  kgnumber of bullets n=278v=0 m/su=977 m/st=13.9 s

Q: Consider the ordered bases B = space V of upper triangular 2 x 2 matrices. a. Find the transition…

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Q: Problem 7. Consider the funcrtion f : R - {1} → R - {1} given by x+1 x-1 f(x) = Show that f is its…

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Q: 5. f(x, y, z) = x z=1-x² X ZA y+z=2 E y

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Q: Let f: R → R³ be defined by f(x) = (8x, –7x, –9x). Is ƒ a linear transformation? f(x + y) = f(x) +…

A: Let  be defined by .We know that a transformation  is a linear transformation, if  and  for all…

Q: What type of graph is this?

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Q: P(x)] B The set B = {− (2 + 4x²), x −6 − 12x², 2x – 4 – 12x²} is a basis for P₂. Find the…

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Q: Problem #1: Find the value of a for which the following matrix is orthogonal. √a √a· ·√a √a+·…

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Q: "S(t-π)dt 1500°

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Q: sin² x x2 goo 88 dx R TT 2

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Q: 2. What point in the feasible region minimizes the objective function? Hint: graph constraints using…

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Q: m This question has four parts. Answer each part correctly to get the next part. We will solve the…

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Q: Factor x4 1 completely in R[x] and then factor it completely in

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Q: Find the standard Matrix Find the standard matrix for the following Q(x) quadratic form Find the…

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Q: 306 3. ³ [34] $[6] 5. 1 -1 3 7. 9. 11. -6-1 2 320 -14 -2 5 3-1-1 -12 0 5 4-2-1 24 4 1-1 3 4. 13-16…

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Q: A. i. Using Arithmetic of Limits, find limn-3n / (5n + 3) ii. Working directly from the definition…

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Q: Exercise: Let u = [3, −2, 1], v = [1, 1, 1] and w = [2, -2,0]. The area of the parallelogram formed…

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Q: Solve the Linear 1st Order O.D.Es:

A: Given that the differential equation is

Q: The set B = {3+4x², 12 − 3x + 16x², 9x - 25 - 36x²} is a basis for P₂. Find the coordinates of p(x)…

A: Here we have to find the coordinates of p(x) relative to the basis B.

Q: 3 Let f: R → R³ be defined by f(x) = (9x, 6x, 5x). Is f a linear transformation? a. f(x + y) = f(x)…

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Q: Please with reduction of order method solve problem boundary value of differential equation…

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Q: Let V = sp({(1, 1, 1, 1)ª, (1, 1, 2, 4)¹, (0, –1, 6, 7)T}) ≤ R4. Find an orthonormal basis {u₁, U₂,…

A: Let (a)To find the orthonormal basis, we will use the Gram-Schmidt process. The formula is

Q: Which of the following transformations are linear? Select all of the linear transformations. There…

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Q: 10. Find the multiplicative inverse of x² + 1 in Q[x]/(x4 - 2). doute

A: This follows immediately using Division algorithm for polynomials.

Q: dz de 02 -13 where dz dt 11 Z + [] 2 2 %3*م and Z [2]

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Q: For A S calculate I+tA+ 0.904837 (-2-6) X 10 -0.200334 X 1.10517 t2 The actual value of e014, to six…

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Q: A given by 1. M₁1 4. M41 12. A = 14. A = 16. A = A = 2-1 3 1 4 13-1 624 1 2 20-2 2. M₂1 5. M34 12 4…

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Q: Let A = A basis for the image of A is -1 −1 1 1 -6 -3 3 6 2 2 -2 -2 Find a basis for the image of A…

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Q: If T: P₁ → P₁ is a linear transformation such that T(1 + 5x) = 2 + 2x and T(4+19x) = 1 +2x, then…

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Q: Let P₂ be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned…

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Q: Let P₂ be the vector space of all polynomials of degree 2 or less, and let H be the subspace spanned…

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Q: olve the system of differential equations given in matrix form for the general solution. We must do…

A: Given that the system of the differential equations i.e.                     Where To find the…

Q: Calculate M5 using a diagonalization process. =[63] has eigenvalues 5, 2. M =

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Q: Given the 2nd order system: x/C1 + L1x'' - My'' = 0 y/C2 + L2y'' - Mx'' = 0 Convert it to a 4x4…

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Q: 1) Given data 1.6 2 8 4.5 f(x) 2 2 a) Calculate f(2.9) using Newton's interpolating polynomials of…

A: Note: We are entitled to solve only one question at a time. As the specified one is not mentioned,…

Q: For the following functions, find their amplitude, period, frequency (reciprocal of the period), and…

A: (c) We have, we know, hence, motion of a particle:Amplitude: Period: Frequency:

Q: Find the slope of the curve y = (x² - 6x-16) at the point (-2,0). The slope of the curve at (-2,0)…

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Q: Using your graph as the example: Select any two points on the graph and apply the slope formula,…

A: The 2-D graph is attached belowTo find out slope we apply slope formula

Q: 3. Here's a way to evaluate due to Euler. We've seen that sin 72 TZ - k² ·ÎI (¹-³). j=1 (a) Equate…

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Q: Let V, W be a pair of vector spaces and A : V → W be a linear image. Then A(V ) is a linear subspace…

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Q: 2. Given the following functions f(t), use the formulas to find the Laplace transform b) f(t)= e'…

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Q: 2 2 4 2 4 b) y" + 2y' + y = | reft - r) dr, y(0) = y'(0) = 0

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Q: 10. Find the remainder of x4 + 3x + 2 after division by x + 3 in

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Q: Problem 4 Let o = (4573) and T = (46823) denote permutations in Sg (a.) Calculate the disjoint cycle…

A: We shall use basics of permutation learnt in abstract algebra