Find the Fourier transform of: x(t)=e=¹² and with this find the value of: Sedt

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Q: M = Find the matrix M of the linear transformation T: R³ → R² given by X1 3x1 = T (1:)) - [³ x2 X3 -…

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Q: IfT: R³ R³ is a linear transformation such that -0-0-0-80-86 -3 T then T -3 - 0 = -2 3 T T = -3 3 2

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Q: (4) Suppose f(x) is increasing on [a, b]. Let Pn = {0, 1,...,n}, where xk = a + k (b − a), k = 0,…

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Q: The cross product of two vectors in R³ is defined by b₁ a₂b3 - a3b₂ 8-0-6-3 b₂ a3b₁ - α₁b3 b3 a₁b₂ -…

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Q: 6 2 3 26 32 38 X

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Q: Use the Maclaurin series for sin(x) to compute 6 sin(2°) correct to five decimal places. 6 sin(2°)=

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Q: T If T: R³ R³ is a linear transformation such that 4 (C) -· 4 then T ([;)) 5 2 = ·(0) - E (9) FE -2…

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Q: Let S be a linear transformation from R³ to R² with associated matrix 2 - [2²2 2 -3 3 0 3] Let T be…

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Q: 3. (8 points) a. How many arrangements in a row of two or three letters can be formed using the…

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Q: 3. Find the Fourier Series expansion coefficients of the following periodic function: 1 if 0≤t<n/2…

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Q: Let S be a linear transformation from R ³ to R² with associated matrix 3 Determine the matrix C of…

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Q: Suppose a system of differential equations can be written in matrix form as dx dt dy dt dz dt = A…

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Q: Solve the initial value problem: x2 dx + 2ydy = 0,  y(0) = 2

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Q: 3. Let V be the solution space of the system X1 + x2 + x3 + x₁ = 0 2x1 + 3x2 + 3x3 + x₁ = 0 (11, 11,…

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Q: Let f(x) be continuous in [0, 1] and f(0) = 3. Find the limit n "St [*^* f(nx²) √nx dx. lim n n→∞

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Q: M Find the matrix M of the linear transformation T: R³ → R² given by T 21 (-8) #3]. −5x₁ + x₂ + (−8)…

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Q: SF. dr, where F (x, y) = (6x − 2y)i +x²7, Evaluate from (6,-3) to (0, 0). and C is the line segment

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Q: Find taylor series of func f(x)=ln(x) at a=10 (f(x)=sum from 0 to infinity cn(x-10)^n

A: Find taylor series of func f(x)=ln(x) at a=10 (f(x)=sum from 0 to infinity cn(x-10)^n

Q: 1. For the system below, find the general solution, sketch the trajectories, being careful to…

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Q: Given that T is a relation on the set {1, 2, 3, 4}, and the set of ordered pairs is: T = {(1, 1),…

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Q: Let A = asis for the kernel of A is -4 6 0 Ia basis for the kernel of A (or, equivalently, for the…

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Q: (5) Define h(x) = x³ sin for x = 0 and h(0) = 0. Show that his differentiable everywhere and that h'…

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Q: ) Find the outward flux of 7 = (x, y², z) through x² + y² + z² = 4.

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Q: 46. kk 0 4 A = ₂² k² 2 k 0 k k

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Q: ∞ x²n-1 2n-1 Let f: (-1,1) → R be defined by f(x) = Σ( − 1) ª−¹. n-1 n=1 Find f'- 2

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Q: 3. Consider the equation for a mass m > 0 on a spring with spring-constant k > 0, with damping…

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Q: Find (a) the orthogonal and (b) a least-squares A = 2 0 1-3 4 1 1 1 1 0 -1 -3 " projection of b onto…

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Q: The matrices A₁ = [J]. - [ ] 4-[61] , 10 form a basis for the linear space V = R²x2. Write the…

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Q: 2. Consider Pell's equation associated to n = 2: x² - 2y² = 1. One of the solutions is N(1, 0) (a)…

A: Given: Consider Pell's equation associated ton = 2 and x ^ 2 - 2y ^ 2 = 1 .One of the solutions is…

Q: How many different photographs are possible if four children sit in the front row and five adults…

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Q: Let A = A basis for the kernel of A is 9 3 -12 - -9 -3 -3 -1 12 4 - Find a basis for the kernel of A…

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Q: Let V = R²x2 be the vector space of 2 x 2 matrices and let L: V → V be defined by L(X) = 15 - || =…

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Q: Show that the equation xy" + y = 0, x > 0, has a regular singular point at x = 0. Determine the…

A: The given differential equation is  with .The given differential equation can be written as:Now…