find the fourier series for f(x) = -#-X -π

Q: x"" (t)- 3x"(t) − 4x' (t) + 12x(t) = 12e-t; x(0) = 4, x'(0) = 2, x'(0) = 18

A: The solution is given as

Q: b) How many non-negative integer solutions are there in the following's expressions? -3 < x < 3 or…

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Q: 6. Show that the closure Ỹ of a subspace Y of a normed space X is again a vector subspace.

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Q: Find the rank of A 1 2 3 A = 149 1 8 27 02 0 3 01

A: Rank: The rank of an m×n matrix is r if the number of linearly independent columns of the matrix is…

Q: ion of the trace of S on the xy-plane, yz entify each trace. he traces obtained in (a). Label all…

A: Given as, 4x2 - (y-3)2 + 4z2 = 4

Q: 1. If x=27-3k and y = 7+57-4k, express each of the following in terms of i, j, k a) 5x-2y

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Q: Theorem 12. Let R is a commutative ring and r e R,fe Hom (M, M'), then rfe. R M, M') defined by (rf)…

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Q: Inverse of a Matrix II. Solve the following 1. Find (1,3) entry of H-¹. 2. Find (3,2) entry of H- 3.…

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Q: A company determines that its total cost, in thousands of 3x rands, for producing x items is C =…

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Q: a = 3i - j - 4k, b = 2i +4j - 2k, c = -i +6k a. 4a - b b. b * (c - a) c. ||a * b|| d. the angle…

A: Solution : Given, a=3i-j-4k b=2i+4j-2k c=-i+6k a.) 4a-b=4(3i-j-4k)+2i+4j-2k =14i-18k b.)…

Q: Find an analytic function whose real part is u(x, y) = x³y - y³x 7²+1

A: “Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Q2) Compute trigonometric Fourier series coefficients of following 2-periodic signal defined on the…

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Q: two nxn symmetric matrices A and B=A+AA, if of A and B₁ ≤ B₂ ≤ ≤ Bn are the eigenvalues of ..

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Q: of the following integral using the Simpson's 1/3 rule will result 0.001. Give the exact answer…

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Q: Let C, D and E be the polar curies below: Cir=f(0) = 3-3 cos 0 E¹r = g(0) = 1/250c4 SOC 3 D:r=3 (1.)…

A: As per the question we are given two curves in polar coordinates as : C : r = f(θ) = 3 - 3cos(θ) E :…

Q: 2 Q) Let A € M₁ C4) such that A² = A ENA show that det (I+A) = 2

A: If minimal polynomial is totally factorizable that is product of linear factors. Then matrix is…

Q: 1) f(x) = zarn 7:0 3-X ·r

A: Solution:-

Q: 2. Find the inverse of A = == CN 2 1 -1 3 - -1 2 2 22 12 3 2 using Gauss-Jordan method.

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Q: Question 4 4.1. Find a power series representation for the function 2x-15 sign, 4.2. determine the…

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Q: sorry but I indicate in the question above that its needs to be transformed into a lower triangular…

A: Given matrix is A = 1-13-1402-2110010-20100011-10   Note:- This is not a square matrix so, we can…

Q: (g) The characteristics of tzr + y = 0 are given by: dy (A) = -1 and dz dy da <=0 (C) = 0 and dy dz…

A: Solution:- option (c) is correct

Q: Consider the following IVP: y'=1+. 1st s2, y(1) = 2. The actual solution of this IVP is y(t)= t…

A: As per the question we have to find the solution to a differential equation using Euler's method,…

Q: 36. Sin(xy) + cos(yz) = 1. Compute z and az at P = (2, п/12,4). дх ду

A: Let us consider the given function z=f(x,y) The partial derivative of the function is obtained as…

Q: The logistic growth equation is represented by the equation: dN Nrmox (1-7) dt =

A: Introduction: There are many different types of population models. All the models are based upon the…

Q: Compute the determinant of the matrix A, below, by using row operations to transform A to an…

A: Given matrices are A=0-5690-6907-970-76-4210-13 B=000000000

Q: 5) Give the surface area and the volume of the shape shown. Show all your calculation neatly. a)…

A: Solution: Let distance between two nearest point in the diagram is a Now, there is a smallest cube…

Q: f(x) = x3 - 2x2 - 15x + 36 = (3 - x)(12 - x - x2) Find the (a)  intervals on which f  is…

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Q: 3. Solve the linear system using Gauss-Jordan method I 2x+y+z=2 y+z+w=2 x+y=z=0 x + 2z-w=1

A: augmented matrix of the given system 211020111211-100102-11

Q: Assume that the Taylor series centred at x = 0 of a function f(x) is Σo anx" Let g(x) = f(x³).…

A: The expansion f(x) is f(x)=∑n=0∞anxn Here a0=1, a2=2, a2=3, a4=4 Since  a0=1⇒f(0)=1…

Q: Let C be the parametric curve defined by [x(t)=t²-t-6, [y(t) = 4t³+31²-6t. Determine the point/s…

A: The general form of a parametric equation of the curve in the xy plane is given by xt=ft and yt=gt,…

Q: In Exercises 23-26, use the shell method to find the volumes of the solids generated by revolving…

A: Note. 1: Since you have asked multiple questions, we will solve the first question for you. If you…

Q: 3. Solve the linear system using Gauss-Jordan method I 2x+y+z=2 y+z+w=2 x+y-z=0 x + 2z-w=1

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Q: 3+z Given the points R (1, -1, -3), the vector v = and the line d: ¯x+¹=1+y= 3 2 3. Calculate the…

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Q: 2. y" - y = x, y(0) = 1, y'(0) = −2, h = 0.1 from x = 0 to 1.

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Q: x² A quadric surface is defined by the equation: + 3y² = 3 + z 3 1. Solve the equation of the traces…

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Q: 2. Given the figure below, find a single vector that is equivalent to C B tw b) 10 14 וד --(A-F+C) G…

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Q: III. Let S be the quadric with equation 4x² − (y - 3)² + 4z² = 4. a. What type of quadric is S? Find…

A: Let S be the quadric with equation    4x2 - (y-3)2 + 4z2 = 4 ⇒x2 - (y-3)2/4 + z2 =1

Q: : R³ → R², find its dual map, where (i) 1(x, y, z)=(x-y, y+z), (ii) t(x, y, z) = (x + y + 2z, 2x+y),…

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Q: (b) One of the following is NOT a second order PDE: (A) Uz Uyy + Uzy=0 (C) (U₂)² -Uz Uy = 0 (B)…

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Q: A value= B value= Horizontal shift:

A: Given,          f(x)=-4cos(x)+2

Q: Given the polar curves: C₁:r = 2 cos 0 π 2 C2 B(0,0) C₁ A(2,0) C₂:r = 2 cos 30 Find the (sum of)…

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Q: III. Let S be the quadric with equation 4x² − (y − 3)² + 4z² = 4. a. What type of quadric is S? Find…

A: Given: 4x2-y-32+4z2=4 To find: Plane

Q: Check the linearity, casualty, stability and the time variance of the following: 1. y(n) = 4 x(n-2)…

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Q: III. Let S be the quadric with equation 4x² − (y - 3)² + 4z² = 4. a. What type of quadric is S? Find…

A: A quadric surface is a graph of the function of two variables x and y in the three dimensional…

Q: Given the vector function (1) = (e+→¹², 2√³+1, 4 arctan(1-1)), find the speed and the equation of…

A: Introduction: Like two dimensional Euclidean geometry, a line can also be drawn in three dimensional…

Q: please could someone solve this for x -415000 =8.314* 1073* ln x

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Q: For every real m x n matriz mx m) and a diagonal m x n matriz

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Q: Consider the following IVP: y'=1+1, 1st s2, y(1)=2. The actual solution of this IVP is y(t) = t…

A: As per the question we are given a first order differential equation as : y' = 1 + y/t  ,  1≤t≤2  ,…

Q: a) Answer the following questions, in how many ways: i) Can we select 6 persons to sit together at…

A: Solution

Q: Find the power series representation for f(x) = 2x (1-x²)² and then find its radius of convergence.

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