Calculate the general solution of the differential equation d²y dx² dy dx -6- +9y = 3x² 16.

Q: 5. Let A be an m x n matrix with real or complex entries. Use the results in the previous Problem 4…

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Q: (1.2.7)List all elements in the following sets. (a) T = {m € Z | m = 1 + (−1)¹ for some integer i}…

A: The sets are: (a) T=m∈Z | m=1+-1i for some integer i (b) U=r∈Z | 2≤r≤-2 (c) U=r∈Z | -2≤r≤2 To Do:…

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Q: Prove that for any prime p > 3, either p = 1 (mod 6) or p = 5 (mod 6).

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Q: 1. Verify that existence and uniqueness results apply to $(2) - S²3²-v "$(y) dy = 0. 2. Show that…

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Q: g(0)=sin 0:

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Q: Diagonalize a matrix to find all functions f (x)and g(x) solving the differential equation: f′(x) =…

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Q: 8. Show that {u,,,,} is an orthogonal basis for R³. Then express x as a linear combination of the…

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Q: Are the statements true or false? Prove or give a counter example. (ii) (Vx)(Vy)(3z)(xz = y).…

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Q: 2. Find the volume of the solid obtained by rotating the region bounded by the given curves about…

A: (a) Required volume                       = 2∫4 πy2dx                       = 2∫4 π{√(25 - x2)}2 dx…

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Q: Consider the second order differential equation Find all singular points and classify them. y" (x) +…

A: A singular point is point when the point is not ordinary point .

Q: For the equation below, show how the left hand side may be simplified to obtain the right hand side.…

A: The given integral ∫241+t3-14t-32dt. We have to evaluate this integral.

Q: 4. Use Green's Theorem to evaluate x²y dx - y²x dy ,where C is the boundary of the region in the…

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Q: Differentiate R (t) = (sint, te, cos 2t).

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Q: Evaluate 1² cos(x/2) x² -dx as an infinite series and find [ - cos(x/2) x² -dx.

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Q: use the graph to determine whether the inverse of f is a unction. Explain your reasoning. 7 11 -6 3…

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Q: QUESTION 3 Let G be a connected graph having the following adjacency matrix: Find the order of G. 8…

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Q: Prove that the following functions are bijections: (a)  f: R → R given by f(x)=ax+b, where a ≠ 0.…

A: Let f:A->B be a function. Injective function: f is said to be injective if different elements…

Q: 16. Find the general formula for the recursive sequence below. an = an-1+2, ao = -2 17. Find the…

A: 16. We have to find the general formula for the recursive sequence:  an=an-1+2, a0=-2 17. We have to…

Q: Given that: (3-x²)y'-3xy-y=0 Find the general term in each solution, if possible

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Q: Find the volume of the solid that lies within the sphere x^2+y^2+z^2=4, about the xy-plane, and…

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Q: A: Prove that a vector (2,-1, 1) is in the vector space W =span((2, 1, 3), (4, 0, 4)) and that (3,…

A: Vector space, W=span2, 1, 3, 4, 0, 4Vectors : 2, -1, 1 and 3, 2, 7

Q: Recall that R* is the set of nonzero real numbers, which forms a group under multiplication. (1)…

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Q: Use a transformation of the graph of y=x to graph the function. f(x) = (x-6)5 +3 Select the graph of…

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Q: 3. A simple graph H is the square of a simple graph G if V (H) = V(G) and xy is an edge in H if and…

A: The simple graph H is the square of another simple graph G if V(H)=V(G). xy is an edge in H if and…

Q: C: Proof that ( a) L (cos²t - sin²t) S s² + 36

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Q: Apply the eigenvalue method to find a general solution of the given system. Use a computer system or…

A: Introduction: The solution of the system of differential equation is obtained by finding the…

Q: 10) Suppose you were given one of thirty free tickets at the beginning of this class period. Suppose…

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Q: 5 We consider a rule. Integrate flx²1= 0.2+25x-200x²+675x² -900ײ + 400ks. single application of…

A: Asper the question we are given the following function : f(x) = 0.2 + 25x - 200x2 + 675x3 - 900x4 +…

Q: It shows wrong

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Q: Q.1 Evaluate Sheet (2) Numerical Integration and Differentiation dx using trapezoidal method to…

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Q: function f(x)=-x^(2)+2x-4, address the ave a maximum or minimum value?

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Q: Find the Fourier Transforms of the indicated function: f (x) = cos x e−x^2/2

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Q: 2(b) Just the answer please. What is the instantaneous rate of change of the function defined by…

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Q: 1-1/2 Find the eigenvalues and corresponding eigenvectors for 3] -2 1

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Q: 3 Let A = -4 eigen value. 7 -5 4 0 Let A 1-3 4 -13 eigenvalue = -2 is an eigen vector of A? If so,…

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Q: Let R 1 show that z" |2|=R 2-1 If īdz| -dz ≤ 2TRn+1 Rm1 for m≥ 1, n ≥ 0.

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Q: The eigenvalues of the coefficient matrix can be found by inspection or factoring. Apply the…

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Q: y" +2y = 2x+5-e-2r y""-6y"=3-cosa

A: These questions are about ordinary differential equation.

Q: f(x) = x^ Is f'(x)=nx-1 Where nER.

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Q: The volume R is the tetrahedron formed by x ≥ 0, y ≥ 0, z ≥ 0,x+2y+3z ≤ 6. The mass density of R is…

A: The tetrahedron is bounded by x≥0, y≥0, z≥0, x+2y+3z≤6 The mass density of R is fx,y,z=x

Q: EXERCISES 8.2.5. Prove each assertion by induction. 3) F4k is divisible by 3, for all k € N†.

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Q: If f' is continuous then prove that lim 1-00 f(x) sin(x) dx = 0.

A: One has to show the limit of the Reimann Integration: