1.- +3 (s-3)(s+5)(s-1)² s2-s+3 2. s3(s+5)(s-2) s-8 3. (s-3)(s²+2s+17)

Q: Is it true that Arg(z) = arctan for x + 0, where x = Re(z) and y = Im (z) ?

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Q: G = (R, +), H = {a+bv2: a,b € Z}

A: Given G = (R, +), H = {a+b√2 : a, b∈Z}. We check whether H is a subgroup of G.

Q: Explain why S is not a basis for P2. S = {1, 4x, -9 + x², 7x} S is linearly dependent. O s does not…

A: Given S={1,4x,-9+x2,7x}. We explain why S is not a basis for P2.

Q: 2. Use the Mean Value Theorem to show that f(r) = 2r sinh(r – 1) +2" – r %3D has a critical number…

A: The given function is: f(x)=2xsinh(x-1)+2x-x. To show: f(x) has a critical point between 0 and 1.

Q: Using Gauss-Seidel Method, obtain the solution to the system; x1 + 5x2 + 3x3 = 30 %3D 3x1 + 7x2 +…

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Q: Use Lagrange multipliers to find the maximum and minimum values of f subject to the given…

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Q: Find the maximum of f(x, y, z) = x + y + z subject to the two constraints x² +z? = 5 and x + r + 6z°…

A: The method of Lagrange multipliers is an approach for finding the local maxima and minima of a…

Q: (3) Suppose an experiment was conducted to identify the exponential growth model of a species of…

A: As per the company rule, we are supposed to solve one problem from a set of multiple problems.…

Q: Q1: Use two iterations of G-S method to solve the linear system. 10x + y+ z = 15.4 2x + 7y + z =…

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Q: (-1)"(n + 2) 2n+1(n + 1) Compute the exact value of n=0

A: The ratio test can be used to assess if a series is converging or diverging. The following are the…

Q: What is the solution of the differential equation y" - 8y + 25y = 36e“ ? %3D O y = C1e-4 cos3x +…

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Q: Denote by C[0, 1] , the space of all continuous functions defined on the unit interval [0, 1]. Show…

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Q: Using separation of variables, solve the differential equation, dy (5 + z10) da Use C to represent…

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Q: y′′′ − 2y′′ − y′ + 2y = e^(−t)sin t by variartion of parameter

A: Given equation  y'''-2 y'' - y' +2y = e^(-t) sin t, say (1)  First we'll find the complementary…

Q: 5. A 1/4-kg mass is attached to a spring whose stiffness constant is 8 N/m. The damping constant for…

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Q: 1. Consider e" for all æ E R. a. Determine the power series representation of f(x) = xe-5a² for all…

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

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Q: For a data set {xi, yi ; i=1,n}, which of the following conditions must be satisfied by an…

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Q: (a) Determine the directional tangent lines to the given function at a given point. (i) f(r,y) = 3…

A: Directional  tangent line to z=fx,y  in the direction of  u⃗=u1,u2   at  (x0,y0) .is the line…

Q: Find the first fundamental form of surface of revolution?

A: Suppose M is a surface determine by , Xu , v ⊂ E3. Suppose αt is curve on M , where t ∈ a , b. Here…

Q: cos40 = 8cos*0 – 8cos20 + 1

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Q: The differential equation dy = 7 + 6 x + 35 y + 30 xy da has an implicit general solution of the…

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Q: How many binary strings of length 10 are there in which the number of 0's in the string is not equal…

A: We have to find the numbers of binary strings of length 10 are there in which the number of 0's in…

Q: Which of the following is/are axiom/s in projective geometry? I. All the points of the plane belong…

A: We have to determine which of the following is axiom of projective geometry.

Q: A = [3 +m ,B = [m land C = [" 10" lFind the matrix X, if -2 14 – m 6 1. Let 8 + m -21 Find the…

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Q: Consider a rectangular plate with width w and hight h. If the temperature at all edges are kept to…

A: Hi! As per norms, we will be answering only the first question. If you need an answer to others,…

Q: s+2 S(s-3) 25 s(s-2)

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Q: 1. Calculate the area of the parallelogram spanned by the vectors Á = and B = .

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Q: Use Lagrange multipliers to find a vector in 3-space whose length is 6/3 and whose components have…

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Q: 1. Let A be an uncountable set and B C A such that there exists a surjective function f : Z+ → B.…

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Q: f(x) = e2* if x> 0 Q5. The Fourier transform of the function: 0 if x<0]

A: We have given a function ,  fx = e-2x , x &gt; 00        ,x &lt; 0 We need to find Fourier transform…

Q: Find the indicated powers of the given complex number. Express the result in polar form, then…

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Q: Problem 1 Find the distance d(v, W) from i = ER' to the subspace W = Span Hint: First check if W has…

A: To find d(v, w)

Q: We want to determine if the sequence n 4+6n is monotonic. Using the difference test we get that sn+1…

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Q: (c) Use the data in the table to evaluate R' (t) dt. n 1 k 1 (d) The sum) R 4 is a right Riemann 2n…

A: For part c we will use Fundamental  theorem of calculus  Part2 If f is a  real-valued function on a…

Q: a subspace of V? Assume that V has the standard operations. W is the set of all functions that are…

A: Subspace of a vector space

Q: Use Lagrange multipliers to find a vector in 3-space whose length is 6/3 and whose components have…

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Q: Prove lim(Vn+1- n)=c 8. 0 =

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Q: -3î + (4 + m)j – k ,č = -9î + 12j – (3 + m)k , ,Q %3D (5 + т,4,0 + m) аnd P %3 (-1,4 + т, —3). Find:…

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Q: Prove: Use the De Moivre's Formula to Prove that for any n greater than or equal to 1 (1+i tan e)"…

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Q: 4х — 6 2. Let f(x) 1- (2г — 3)3 (a) Find the Taylor series representation for f about x = 1.5 that…

A: We have to find the power series and approximate f(1.55).

Q: Find the amount of salt in each tank according to the following diagram. The initial volumes are 3…

A: Given: Initial volume in both tanks vx=vy= 3gallons. x(0)=1 y(0)=0 vx- volume in first tank…

Q: dy Find the solution to the differential equation da 6xy (In y)² which passes through the point…

A: Given differential equation is dydx = 6xy(ln y)2

Q: If we do not discuss orthogonal diagonalization, you may omit this probl Let A be any m × n matrix.…

A: Let , A be any m × n matrix. We need to show that , AT A has an orthonormal set of n eigenvectors.…

Q: If L is a line in 2-space or 3-space that passes through the points A and B, then the distance from…

A: Find the distance from the point P(-3, 1,4) to the line through A(1, 1, 0) and B(-2, 3,-4).

Q: Solve for the approximate value of (z² + 3z + 6) dx at n = 5. Solve also the true value of the…

A: To approximate the given integral by using trapezoidal rule.

Q: Sy" + 5y' + 6y = 0 ly(a) = 0, y'(a) = 1, (a > 0)

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Q: 1+ 2n² Xn {Tn} 1– 3n2 - Prove that the sequence where is bounded.

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Q: Through the point (2, -4, 0) and parallel to each of the planes 2x + y -z = 0 and x+ 5y + 3z = 0.

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Q: An inverted pyramid is being filled with water at a constant rate of 25 cubic centimeters per…

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