(0 1. f(x) = 6 0 Find the Fourier series (ao, an, bn and the fourier series formula) if-2 < x < -1 if-1 < x < 1 if 1 < x < 2

Q: a. Solve the ODE y" + 3y + 2y = 0. b. Use the method of undetermined coefficients to find a…

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Q: 5/ change the cartesian integral in an equvalant polor integral then evalute 2x-x² the polor…

A: First we change x and y into r, theta form means polar coordinates  x=rcos(theta) y=rsin(theta) Then…

Q: In the group Z24, let H =(4) and N=(6). (a) State the Second Isomorphism Theorem. (b) List the…

A: Given  Group is  Z24 , let H=4 and N=6

Q: In the group G = Z24, let H = (4) and K = (8). (a) State the Third Isomorphism Theorem. (b) List the…

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Q: Q5: Find the general solution for the following second order differential equation: y" - 4y' + 4y =…

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Q: Q5. Solve the following by using Inverse Laplace Transform (i) s² S4-1 (ii) 3s-14 s²-7s+10

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Q: cubic

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Q: ensor analys

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Q: We consider the following differential equations: xy" + xy' - (x − 3) y = 1 pour x > 0. Give the…

A: Consider the following differential equations: xy''+xy'-(x-3)y=1 for x&gt;0   To Find: General form…

Q: Find the optimal solution to the following problem. Minimize f (x1, X2, X3) = x₁² + 2x2² + 10x3²…

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Q: (d) (i) Factorise the quadratic expression x² + 3x - 28. 22 (ii) Use your answer to part (d) (i) to…

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Q: In Mathematics one of the assessment methods is journals, by using an example explain this method…

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Q: (a) Use sigma notation to write the Maclaurin series for cosлx.

A: Please see the attachment  According to the guidelines we are supposed to do one problem.

Q: The set H={0,1,2}is a subring of (Z4, +4,.4) integer ring module 4. От O F

A: Answer is given below in the Step-2 box. So, the statement is false.

Q: Solve 2-D

A: Introduction:   A differential equation is an equation that contains the derivative of an unknown…

Q: In the group G = Z₂24, let H =(4) and K = (8). (a) State the Third Isomorphism Theorem. (b) List the…

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Q: The following table shows the daily receipts in millions of dollars of the movie "Avatar" for…

A: Instantaneous rate of change is the slope of the given data . So, basically we have to find the…

Q: Find the optimal solution to the following problem. Minimize f (x1, x2, X3) x₁² + 2x2² + 10x3² s.t.…

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Q: Let X be co or lº, 1 ≤ p ≤ ∞o. Consider the operator Prove that U is not compact but U² is compact.…

A: Please find the answer in next step

Q: 2 Express (+) in polar form O 3 [cos 67+isin 67] O 13 [cos 70+isin 70] O 3 [cos 70+isin 70] O 13…

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Q: Q.5. If we have two vectors (V₁ and V₂), V₁ is a vector perpendicular on the plane passer through…

A: Introduction: When a vector is along the direction in another vector, the two vectors are parallel…

Q: Use the Divergence Theorem to calculate the surface integral 11. F F. ds; that is, calculate the…

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Q: Solve the following problem. If answers are not whole numbers round off to the nearest hundredths.…

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Q: [[F. F. ds for the given vector field F and the oriented surface S. In other words, find the flux of…

A: To find- Evaluate the surface integral ∬SF·dS for the given vector field F and the oriented surface…

Q: Find the residue of 3 Z Z²-1 at z→ ∞

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Q: 3. Find the solution of the following system of liner inequalities by graphing- (K + 2y > 5x + 3y…

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Q: A population of termites doubles every 0.35 days. The initial population is 1800 termites. a) How…

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Q: : Find the divergence of the vector field At the point (2,4,1). F(x, y, z) = x² √yi+j+zk

A: We have to find the divergence of the vector field F(x, y, z)=x2y i^ +yxj^+zk^ at the point (2, 4,…

Q: Consider the vectors x(¹) (t) = ( ) and x(²) (t) = ( 6 ). 6t (a) Compute the Wronskian of x(¹) and…

A: “Since you have posted a question with multiple sub-parts, we will solve first three subparts for…

Q: of the periodic function f(x) given

A: To find- Find the Fourier coefficients of the periodic function fx given below and find the Fourier…

Q: Choose the wright answer of: Z(7)* O 7z/(Z-1) O 1/(z+7)

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Q: Let K be integer ring module 12 and let 1=([4]) and J=([6]) be ideals of K. Then ([0])

A: We have given a integer ring module 12 which have given two ideals I and J  so first we find the…

Q: -<t <-/ Let f(t) be defined as f(t) = t -<t</ TU TC <t<n Extend f(t) periodically and find the…

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Q: Find all values of z satisfying the given equation. e² = 21 Z= n = 0, ±1, ±2, ...

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Q: xed overhead ts of Php440 of Php per un

A: To find the profit or loss of manufacturer as,

Q: Suppose the graph is planar but not connected, and has 5 components. Derive a variant of Euler's…

A: As per the question we have to derive an alternate Euler's formula in case of planar but not…

Q: Find with sketch the Fourier coefficients and Fourier series of the function fx) defined by f(x)= x²…

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Q: Research work : Power series of Ordinary Differential Equations

A: Introduction: The majority of ordinary differential equations are tedious and complex, and they…

Q: 6. Find the Laplace transform of the following functions (c) g(t) = = cos 3tH (t-π)

A: The Laplace transformation is very significant integral transformation that is used widely in many…

Q: 582 28s - 26 (s+2) (S-2) (5-2)

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Q: 2. Consider the following IVP y" + 5y +6y=0, y(0) = 2, y'(0) = 3. (a) Write the ODE as a system of…

A: Given: y" + 5y' + 6y = 0  To find: Solution

Q: ¹).. Suppose that fn are integrable and ffn du <∞. Show that, if fn 1 f, then f is integrable and f…

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Q: 66.5 sq. m. What is

A: Given as, Stations 5+100  Stations 5+120 base width 12 m area of 5+120 is 66.5 m2 volume between the…

Q: We consider the following differential equations: xy" + xy' - (x-3) y = 1 pour x > 0. Give the…

A: Given differential equation is xy''+xy'-(x-3)y=1    for  x&gt;0   To Find: A general form of the…

Q: Q5/ change the cartesian integral in an equvalant polor integral then evalute 2x-x² 1 the polor…

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Q: Consider a matrix A with m rows. Which condition below will ensure that every vector in Rm is in the…

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Q: Evaluate the following double integral using the composite Simpson's 1/3 rule with one interval in…

A: To find- Evaluate the following double integral using the composite Simpson's 1/3 rule with one…

Q: show that the following function @f(z)=3z²+57-6 are analytic

A: Sol

Q: (5) In commutative ring with identity each proper ideal is contained in prime ideal. От F

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Q: vb cu Pop ()) c= (WA EXAMPLE 3.1 In a one-dimensional infinite solid, -∞<x<∞, the surface a<x<b is…

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