[2] Find the Fourier series of the function f(x) = sin(4x) {ain(kx) -T≤ x < -π/2 -π/2

Q: Two mutually exclusive events A and B have probabilities P(A)= and P(B) = Find P(AUB).

A: as per our guidelines we are supposed to answer?️ only one question. Kindly repost other question as…

Q: - x, then answer the following ( (1) Find the function's domain (2) Find the function's range. (3)…

A: Note: Hi! Thank you for the question, as per the honor code, we are allowed to answer three…

Q: DEICH Q2: If P(A)=0.25, P (B)=0.45, P (AB)=0.43, draw the Venn diagrams and determine the following…

A: To find the given subparts using the given condition :-

Q: Q5: (A) If the matrix A = [3 5 7; 10 11 12; 2 4 6; 13 14 15], find (5 only) ( 1. A([2 3],[21]) 2. A…

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Q: Equation: f(x)=2x-x-1.7 Tolerance: x10-5 Assume x = 0; b=2

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Q: Find the particular solution to the differential equation: 2(y')² ( y" = 1- when +3) x = 0, y = 1…

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Q: (9) 2z+p²+qy+2y² = 0 z=ax- 2 2 +c -2 + C₂

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Q: Find the general solution of (D²-7DD' + 12D'2)Z = sin(x - 2y) + ex-2y

A: This question is from linear partial differential equation.

Q: x1 + 5x₂ + 3x3 = 30 3x1 + 7x2 + 13x3 = = 80 12x1 + 3x25x3 2 (0) (0) with ¹ [x(0), xQ), xº)] = [1, 2,…

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Q: Check the stability of the following system using the given Lyapunov function? 0+0+Sin e-…

A: see my solution below

Q: dy Q2/ Use Euler's method to solve + 1.2y = 7e-0.3x from x = 0 to x = 2 with the initial dx…

A: The solution is given by using the Euler method with 4 decimal places as below.

Q: (b) Express the following function in terms of unit step function (1 0≤t<1 f(t)=2-t 1≤t<2. t≥2 Hence…

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Q: Q3: A Cummins diesel engine is available in heavy-duty pickup trucks. The probability of the engine…

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Q: Q3 The boundary value problem governing the deflection of a beam of length three meters is given by…

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Q: For each of the following equations, state the order and tell whether it is nonlinear or linear, In…

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Q: 5. Use Cartesian coordinates to evaluate JIJ y² dv D where D is the tetrahedron in the first octant…

A: Find the proper limits for the triple integral, then integrate.

Q: By direct partial integration, Solve the following 5 4 PDES 8- • Xd²z dz dy ₂ Z(X₁0) = x +X, Z (2,…

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Q: Solve the problem PDE: Utt=9UTT 9urz ВС: IC: u(x, t) = help (formulas) 00 u(0, t) = u(1, t) = 0…

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Q: Evaluate  f '(3). Also, find the two-point forward difference, two-point backward diffrence and…

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Q: Next question Find the volume of the solid whose base is the region in the xy-plane that is bounded…

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Q: Q2: If P(A) = 0.25, P (B)=0.45, P (AB)=0.43, draw the Venn diagrams and determine the following…

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Q: 1. Identify the surfaces of the following equations by converting them into equations in the…

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Q: - complete solutions.

A: The co-ordinate related as x=rcosθy=rsinθz=zx2+y2=r2θ=tan-1yx Then,…

Q: At 8 a.m., you place a certain amount of bacteria on a slide. Every hour, the area covered by the…

A: Given, Time for placing bacteria is 8 A.M. Every hour, the area covered by the bacteria is doubles.…

Q: 1. Consider the following statement about three sets A, B and C: If An (BUC) = 0, then An B = 0 and…

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Q: Determine whether the following ordinary differential equation cosh (3/y) - In(7y)y" = 11cos(4yx) -…

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Q: By direct partial integration, Solve the following PDES 8- X 8²Z 5 4 dz z(x,0) =X+X, Z (2,y) = 3 y z…

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Q: Let p= "It is extremely humid." Let q= "It will rain tomorrow." Convert into symbols: a. "If it is…

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Q: Gaussian Elimination Equations: 3X1 - 2x2 + x3 = 4 2x1 - 5x3 = 1 -3x2 + x3 = -1

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Q: the volume of the solid B that lies above the cone z = √√x² + y² and below the sphere x² + y² + z² =…

A: We will use relation between cartesian and spherical co ordinate to set up triple integral for…

Q: How many positive integers less than 1,000,000 have a digit sum of 5

A: We have to find the number of positive integers less than 1,000,000 have a digit sum of 5. We know…

Q: Find the general Solution of the following PDES • 3 их + 2 Иу U (x₂0) = 4x 2 e (3y-2x)/2 ans- u(x,y)…

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Q: (6) z² = pqxy z = c+xªy/a

A: Let us consider the PDE F(x,y,z,p,q)=0 The charpits formula is…

Q: b) Find the area between the 2 curves f(x) = x² +4-4x and x- with the two lines = 5 & x = 2. axes…

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Q: (b) Show that the continuous image of compact set is compact but the convers need not to be true.…

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Q: 8 {4} {{ {}₁ s² + a² s² +6² (1)

A: We have to find the value of a+b.

Q: Consider the following statement.       "If (n+1)2 is an odd number then n is an even number." (a)…

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Q: b) Find the area between the 2 curves f(x) = x² + 4 − 4x and x - axes and border with the two lines…

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Q: * Please write explanation and don't use calculator Consider a damped spring-mass system with ? =…

A: Given,m=1kg, k =4kg/s2 ,b =5kg/sand ω=2rad/s

Q: Find the particular solution to the differential equation when y(0)=3 and (2)=1

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Q: Exercises: 1. An object moves in space with acceleration. +4j+(4-t)k. alt (t) = -ti When t = 0, it…

A: i. Here we have given that the acceleration on an object is, at=-ti+4j+4-tk we know that, vt=∫atdt…

Q: 3: A) Find the limits below x² + sin²y 1) lim lim (x,y) →(0,0) 2x² + y² y)→(1,1) x#y (x²-y² (x, y) =…

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Q: no of edges for a tree with number of vertices 10 is

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Q: Identify the surfaces of the following equations by converting them into equations in the Cartesian…

A: (a) Given equation is z2= 4+4r2  ......(1) The equation is in cylindrical coordinates. The…

Q: = Solve the recurrence relation an 7an-1 12an-2 for all integers n ≥ 2, a₁ = 1 and a₁ = 6.

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Q: Q3: A Cummins diesel engine is available in heavy-duty pickup trucks. The probability of the engine…

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Q: Let Xis Hilber - Ⓒ || T* ace 2 T* || =)) + |1²

A: This is a problem of Functional Analysis.

Q: sing cylindric -2²2², 0≤ solid B that 2 = 2 using s

A: 6. (a) The required solid is R=x,y,z: 0≤x≤1, 0≤y≤1-x2, 0≤z≤4-x2+y2. In cylindrical coordinate…

Q: 1. Use de Moivre's theorem to find all solution to 25 +32i = 0. Give the solutions in polar form…

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Q: c). Evaluate √√x² + y² ds along the curve r(t) = (4 cost)i + (4 sint)j +3tk, -2x≤t≤2π.

A: We solve the given line integral.