2. Consider the eigenvalue problem, y" + ày = 0, for 0 < x < 1/2; y' (0) = 0, y(n/2) = 0. Find all eigenvalues and eigenfunctions for the case where the auxiliary equation has complex roots.

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A: We have to describe the transformation and sketch both f(x) and g(x).

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A: Rational root theorem

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Q: 3. Find the derivatives of y with respect to x: a) y = xex - e* %3D b)' y = e(4x+;) c) y = e*(sin x ...

A: To find- Find the derivatives of y with respect to x: y = xex - x y = e4x + 1x y = exsinx + cosx y ...

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A: Geometric series

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A: Definition of the definite Integral

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A: To Prove: ∫γf(z)(z-z0)2dz=∫γf'(z)(z-z0)dz Now, let us consider g(z)=f(z)z-z0  

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Q: Quèstion 2 Determine whether the given sequence converges or not. If it converges, find its limit. n...

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Q: 1. Let f and g be continuously differentiable functions. PROVE: div(fvg -g v f) fag gAf %3D Hint - U...

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Q: d) Determine whether ) (an + bn) is convergent or divergent. n=1

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Q: 2. Find the interval and radius of convergence for series Lk=1

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Q: Exercise 1: Directions: Evaluate the following integrals. Show your complete solutions. Identify the...

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Q: 1 2 2 1 4 2 7 5 2 -1 4 -6 3 1.

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A: Here  sin(x) - x/2 = 0Let  f(x) = sin(x) - x/2 ∴ f′(x) = cos(x) - 1/2 Let x0 = π2 

Q: Let B = {1,2,3}. We construct a graph G = (V, E) on n = 6 vertices with vertex set V = P(B)\{0, B}. ...

A: Given B=1,2,3. Consider a graph G=V,E, whose vertex set is V=PB\ϕ,B. Since B=1,2,3, therefore PB=ϕ,1...

Q: 13. S 5x dx x5-3

A: To integrate ∫5x4x5 - 3dx

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A: This is the problem of application of differentiation, Rolles theorem.

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Q: Consider the system of linear equations :) -- ( ;) 3 1 8 5 In the following, let A denote the coeffi...

A: The explanation is as attached:

Q: Suppose E-1 an and E=1 bn are series converges absolutely. Prove or give counterexamples for the fol...

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Q: 4. Use synthetic division to divide 4x- 24x+ 18x + 6x + 29 by x- 5. Express in terms of quotient, di...

A: Synthetic division

Q: Sólve the following differential equations: Homework V1-3x 1 dx+ sin y (a) (b) xy+x Inx=1-3x Cos 2y+...

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Q: Question 2 Determine whether the given sequence converges or not. If it converges, find its limit. n...

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Q: Obtain a series expansion for the integral 1/2 1/(1+x*) dx and justify your calculation.

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Q: b.) Show that if a and b are positive integers where a is even and b is odd, then (a,b) = (a/2, b). ...

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Q: fer)=X-8. .25+ X² 2 What is the derivative of the following equation?

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Q: Let S be the surface described by the vector function Ř(u, v) = (v², u + v, e²«). Find an equation o...

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Q: b.

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A: A triangle is a plane figure with three angles and three sides. If three sides of a triangle are pro...

Q: 10. Consider the basis B' {u1,u2},B = {V1,V2} for R2, %3D where u1 = U2 = V1 = V2 = (a) Find the tra...

A: Change of basis : A transition matrix  P (also called base change of basis matrix), makes any vector...

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A: We will make a table for income statement 

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Q: 3. Solve the following systems of equations. 4y + 3z = -7 12x - 3y + z = -7 -6x + 2y - 2z = 12 4. Di...

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Q: 3n + 2n + 1 1, test for convergence or divergence, using each test ermining Convergence or Divergenc...

A: We have to check whether given series is convergent or divergent.