Use induction to prove 12 + 22 + · . . + n² n(n+1)(2n+1) 6.

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Q: 4-2. (a). What is the coefficient of x7 in (1–x)9 (b).What is the coefficient of x in (1–x)-9

A: We have to find the x^7 coefficient.

Q: luplace transforms Cosht COS!

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Q: (b) Obtain the general solution of y^ prime prime +2y^ prime +y=e^ -x ln x on (0, ∞)

A: To find- Obtain the general solution of y'' + 2y' + y = e-xlnx on 0, ∞.

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Q: 4-2. (a). What is the coefficient of x in (1-x)9 (b).What is the coefficient of x' in (1–x)-9

A: (a)  We need to find coefficient of x7 in 1 - x9. We know that , binomial theorem ,  a + bn = ∑i=0n…

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Q: 5.) Let B = {(1,1, –1), (1,–1,1), (-1,1,1)}, and B' = {(1,0,0), (0,1,0), (0,0,1)} be bases for R³,…

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Q: Q1. Solve the initial value problems: (Ь) y + 2ry + xy' = 0; y(0) = 1 %3D

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Q: 2. Let A:= {1,2,3, 4} =: B and T:= {(a, b) € Ax B | e Z}. (a) Find A x B. (b) Find T (c) Check what…

A: Given: A=1, 2, 3, 4=B and T=a, b∈A×B : a+b+12∈ℤ To find: a) Find A×B b) Find T c) Check what…

Q: In Problems 7-12, solve the matrix games using a geometric linear programming approach. 2 -3] 2] 2…

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Q: the initial value problem (y2 – 1)y' – a² – 1 = 0 with an initial condition of y(0) = y0 in the…

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Q: Consider the equation of the surface S given by -2x" - yPz° + xy = -4, where a is an odd number and…

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Q: In Exercises 9-12, show that the Gauss-Seidel method diverges for the given system using the initial…

A: We can solve this using gauss Seidel method

Q: (b) Determine the following Laplace transforms: (ii) mathcal L \ cos 1 2 t sin 1 2 t\

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Q: 20 (1). Consider the equation of the surface S given by -2xyz + xªz² + 3yB = 2, where a is a %3D odd…

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Q: tz = 0,1 · X 0,1 - Y ty=1 0,1 - (Y + 1) si X = Y si X +Y ti = mín(t, ty) tą = máx(t,, ty) vo =…

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Q: Evaluate the given Laplace transforms. (Write your answer as a function of s.) L{1} %3D L{t} Use…

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Q: determinar todas las raices de la ecuacion (z-2i)^3 = -1+i

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Q: If A=2(1-cos 0)â, – pyâ, (1– cos ¢)â, – ppâ, +zcos² þ⸠, what is 4 8. V•A ?

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Q: Solve the first order differential equation by separating variables

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Q: 13 (2). Consider the problem of maximizing the algebraic expression q given by q = V6 - (I+ 2)2 – y?…

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Q: а. Complete the basis step of the proof.

A: To prove that:              ∑i=0n2i=2n+1-1  for any nonnegative integer n.

Q: Differentiability of f(r,y) at point (a, b) Let f : R? R be a function given by ry if (1,9) + (0,0),…

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Q: ) Obtain the general solution of y" + 2y + y = e² In r

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Q: U sing induction ,prove that : can+1)! for n>o (1) (3)(5)... (an+1) = a" n!

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Q: Advanced Math (a) Use the two step AB method with h = 1 to approximate y' = ty for 0 <t< 3 and y(0)…

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Q: Q3. Find the solution ylt) of the initial value problem (1) Hat =0, l0\ = | Where ə is o postve…

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Q: Let f : A → B be a function. Prove that f is surjective if and only if, for every pair of functions…

A: Please comment if you need any clarification. IF you find my answer useful put thumbs up. Thank you.

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Q: ry? V1+ x²

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Q: Let f: R2 → R be a function given by x²–y² if (x, y) # (0,0), f(x, y) = if (x, y) = (0,0). Using…

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