2. sin x 3. dy dt dy dx + y cos x + 2xey + y² cos (2t) = 0 4. t²y' + 2ty - y³ = 0 - (1-x²ey) dy dx 3x² = (1-x²ey) y (0)=1

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A: Please find the attached image

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Q: 2.15 Find a graph G with 10 vertices, 24 edges and Y(G) = 4. 10 2193

A: Please find the attached solution

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Q: If G is a group and H is a subgroup of index 2 in G show that H is a normal subgroup of G.

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Q: Define f: [1,00)→ R by f(x) = (-1)"/n for all z € [n, n+1). Prove that (a) f exists; (b) f is not…

A: Please find the attached solution

Q: (c) Let R be a finite commutative ring with identity. Prove that an ideal in R is prime if and only…

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Q: 8. Show how the Gaussian quadrature rule can be used for a [₁1(a), 5 dr-f - V ( -√² ) + ( + √(√² )…

A: Given : I=∫abf(x)dx To prove : ∫-11f(x)dx≈59f-35+89f0+59f35 To find : ∫0π2 x dx

Q: Chapter 6, exercise 4.1: Write the product x²yx-¹y-¹x³y³ in the form x¹y¹ in the dihedral group Dn.

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Q: Minimize z = 3x + 4y 4y+ 6x > Subject to 2y + 2x 3y + x > ● ● x IV IV Y 0 Solve this using the…

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Q: -(t-2) 2 EX) If filt) = rec (+-²) and fa(t) = 2 e u(t) find filt) & f₂ (t)

A: please find the attached solution

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Q: a) Prove that every integer can be written a sum of powers of 2. b) Write 14, 17, 27 as a sum of…

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Q: the equation to the plane in the new position is ax + by ±z √√a²+ b² tan α = 0.

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Q: a = 3 iff N(a) = G. also show that if G is finite, then a € 3 iff o(N E

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Q: 2. y+3y"+4y+2y=0; y(0) = 4; y'(0)=-4; y"(0)=1 a. y=e* (4+sin x) b. y=4e¹ cos x c. y=e*(1+3 cos x) d.…

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Q: D(G) If G is a finite group, than o(G) = Σ- o(N(a)) where this sum is taken over one element of each…

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Q: In which option can you find a linear independent set of vectors? {(1, 1, 1), (0, 0, 0)} {(1, 0, 0),…

A: As per our guidelines we can answer only first three subparts and rest can be reposted. Linear…

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Q: Assume that 0 0, consider the sequence of sets: A₁ = {\fn-f|> }, n=1,2,... (1) Show that, for every…

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Q: Question 4. A circle centered at (0,0) with radius one is revolved about the line x=3. The solid of…

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Q: This extreme value problem has a solution with both a maximum value and a minimum value. Use…

A: Given function is fx,y=x2+y2+z2 and contraint x4+y4+z4=7. To Find : Extreme value of the function…

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Q: Question 2 differential equation 1 = 1² + Consider the following 2 = 14e-41 y−3 a) Is the given…

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Q: By using the substitution ² = 2 sec 0, show that f da x√x¹4 = arccos (2) + + c.

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Q: 2. We say that an element z E F is a square root of a E F whenever 2² = a, we denote the square root…

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Q: (1) Let E= R, fn = X[0,1], and f = X[1,2]. Check which converse implications do not hold in Question…

A: Please find the attached image.

Q: Find the reference number for the following angle (in rad unit) (a) 117 (b) - 4 (c) 4 (d)6 101T

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Q: A function is given by f(x) = 2x - e-6. Now answer the following: (a) Approximate the derivative of…

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Q: Assume that now = R. Show that x.x=0 [Hint: Differentiate constion't ev]. Deduce that I is a…

A: Please find the attached solution

Q: If G is a group and H is a subgroup of index 2 in how that H is a normal subgroup of G.

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Q: Suppose b is changed to b' . How large relative change can this change produce in the solution to Ax…

A: The given matrix is, A=1112501-12,  and b=123. To Find: The maximum change in the solution of the…

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