i) Prove that the series sin nx n2 n=1 converges pointwise on R, and uniformly on any finite interval.. Call its sum f(x).

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Q: Solve the following homogeneous problems 3 u(1,t) — и (2, t) —0 u(x 0) =x- 1

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Q: Find a power series for the function, centered at c. 1 h(x) c = 0 8x' %3D Σ h(x) : %3D n = 0 Determi...

A: It is given that fx=11-8x. We have to find the power series representation of the form ∑ an of the g...

Q: Consider the following. u = (0, -4, -2), v= (5, -1, 1) V (a) Find the projection of u onto v. (b) Fi...

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Q: OET 2. Answers must be in RECTANGULAR FORM. 1. Evaluate every equations given. 3. BOX your FINAL ANS...

A: We are authorized to answer one question at a time, since you have not mentioned which question you ...

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Q: 3. You and your roommate, a mechanical engineer, each modelled the heat transfer of an industrial pr...

A: When both temperature will be same then,1001-e-0.2t = 40e-0.01t⇒1001-e-0.2t- 40e-0.01t = 0Let, f(t) ...

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Q: n2n n=1 (1+n)³n converges O diverges

A: It is given that ∑n=1∞ n2n1+n3n. Let us denote the general term of the series by un. So we get, un=n...

Q: 2. Notando argued that the series 1- is alternating. Tando disagreed. Which of the two will you agre...

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Q: Theorem 6: Multiplicative Property for Determinants If A and B are nxn matrices, then det(AB)= (det ...

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Q: 3. Compute a basis for the column space, row space and nullspace of the following matrix. 1 -10 -1 -...

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Q: -1 2 What valuls e a, b, c,d that that mwhe this - 1 - 5 5 consitents - 2 A xc B --- ~

A: We have to check whether given system is consistent or not?

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Q: The 4th term in the expansion of (2x² – 3x)* is - 10 Ca (2r²)*(-3z)® O 10 C4 (2a²)°(–3x)“ O 10 C3 (2...

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Q: Task 2: Analyze the graphs of the polar equations r= acos(ne) and r= asin(ne) when n is an even inte...

A: Solution: Part (a)     The maximum value of r is a.   Part (b) sketch the graph when n = 2    

Q: A small community wants to buy small vans and small buses. for your public transportation system. Th...

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Q: [101 If A = 1 1 and b = |0 li 2] a. Find £. b. Find the projection of b onto the column space of A (...

A: In linear algebra, an idempotent matrix is a matrix which, when multiplied by itself, yields itself....

Q: Use the functions f and g in C[-1, 1] to find (f, g), ||f||, ||g||, and d(f, g) for the inner produc...

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Q: Let A and B be sets. Show that A∪(A∩B) =A using a traditional verbal proof, a series of equalities t...

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Q: nach limits to show that the space ℓ∞ is not reflexive.

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Q: The maximum carrying capacity of a park is 100 animals. Currently, there are 10 animals in the park....

A: Given : r=0.001

Q: Given the points M(0.1, -0.2, -0. 1), N(-0.2, 0.1, 0.3), and P(0.4, 0, 0.1), find: (C) the scalar pr...

A: We have to find the scalar projection and angle between vector.

Q: Problem 2. Find the volume of the paralellepiped with one vertex at P (1, 1, 1) and deter- mined by ...

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Q: 3. Let f(г) — 1+х+z? + 23 + 4 + 25. (a) definition of Taylor polynomials. Find T3(x), the Taylor pol...

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Q: An+1 7. Recall the special case of the ratio test, which is inconclusive if lim equals one. Prove An...

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Q: Use Lagrange multipliers to find the point (a, b) on the graph of y = e9, where the value ab is as s...

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Q: 21 The fnn tois represented in the following tabile. Give the best estimate for | f(x)dx 9. 15 21 27...

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Q: | 7. Find the solution to equation (1) that satisfies the initial conditions y(T/2) and y (T/2) = 0....

A: We can solve this using ordinary differential equation ,in this question first we solve complementar...

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A: Given that x+60p=3500 We have to find affected revenue. 

Q: [20] Find the general solutions of 4y" – y = 8et/2 2+ et/2

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Q: 5. The Fibonacci numbers are defined as: fo = 0 , fi = 1 , and fn = fn-1 + fn-2 , for n > 2. Give a ...

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Q: 5. The race for the governor of Vermont, suppose the state vote was as follows: Marilyn Christian Ho...

A: By the given data we can see  Howard Dean got majority votes. Howard Dean got 52.3% of total votes.

Q: Prove that f is an identity function of itself.

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Q: Let M be a closed subspace of a Hilbert space H. Prove that MnM = {0} and that every h in H can be w...

A: If M is a closed subspace of H, we define its orthogonal complement as  K⊥=h∈H | h,f=0 , for all f∈M...

Q: [32] Consider the initial value problem y"(t) + 2y'(t) + y(t) = 8e*, y(0) = -3, y'(0) = 2. (a) Trans...

A: Solve the differential equation, by using Laplace transferom.

Q: Use the Geometric Series Test to show that 0.3+0.03+0.003 +… converges.

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Q: 10 Find the inverse of matrix A -31 A: -8 a) 59 l-1 3 -7. 1 [ 8 31 b) L 59 l-1 1 [8 c) 59 3 -1

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Q: Let A = {1, 2, 3, 4, 5}. Define a relation on the power set P(A) by declaring that (X, Y ) ∈ R if an...

A: Let A be a non empty set, A relation R on A is said to be an equivalent relation if  1) R is reflect...

Q: HW9_1 Linearize the model y = a x eP* and solve for the coefficients by hand using the following dat...

A: The given equation is written as follows: y=αxeβx                   ...1

Q: Let f(z)=y-2xy +i(-x+x² - y²)+z² where, z=x+iy is a complex variable defined in the whole complex pl...

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Q: 1 an 3sin2(n) The series converges. O The series diverges.

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Q: dy (x + 1)+ y = In x ;y(1) = 0 %3D

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Q: dy - 4 - 5y = dy -3t sin(4t) ; y (0) = 3, y (0) = 10 dt2

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Q: raluate the iterated integral by converting to polar coordinates. 16 – x2 (x2 + y2) dy dx dr de =

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Q: Find the Taylor Series for the following functions:

A: According to our guidelines we can answer only one question and rest can be reposted. 

Q: 4 If A is a symmetric matrix, then At = |A| O A diagonal matrix

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Q: Are the vectors and linearly independent? 3 Choose f they are linearly dependent, find scalars that ...

A: We want to find the vector are linearly dependent or independent.

Q: The interior of a building is in the form of a cylinder of base radius 12 m and height 3.5 m surmoun...

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