Find the Fourier Transforms of the indicated function: f (x) = cos x e−x^2/2

Q: Graph the polar equation below by moving the points. r = 6 csc (0)

A: Let P(x,y) be any point in Cartesian co-ordinate. Then in polar co-ordinate system  x=rcosθ ,y=rsinθ…

Q: Evaluate ozy ds where S is the portion of the plane x+y+z=1 that lies in the 1st octant and is in…

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Q: The following matrix is the adjacency matrix corresponding to a directed graph. Determine if the…

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Q: Find the line integrals of F = 4yi + xj + 2zk from (0,0,0) to (1,1,1) over each of the following…

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Q: The matrix A₁ = -4; 7₁ A = has the following eigenvalues and eigenvectors = -6 (₂₂) 2 2 3 (-1); A₂ =…

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Q: Which number line represents the solution of m+ 3 < 10? A C. O A B OD 5 6 7 8 9 10 11 12 13 14 15 +…

A: The inequality :m+3&lt;10

Q: # C G H Consider the graph given above. Add an edge so the resulting graph has an Euler path…

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Q: (d) Compute the least common multiple of 336 = 24.3.7 and 180 = 2².3².5. Include an explanation of…

A: The given number is 336 and 180. To find the Least common multiple can be obtained by the prime…

Q: Find the final amount in the following retirement account, in which the rate of return on the…

A: Future value of ordinary annuity is  FV=R1+in-1i Where 'R' is regular deposit, 'i' is periodic…

Q: Consider the autonomous differential equation = P(100P), which could be used dP dt to model the…

A: The given differential equation is, dPdt=P(100-P). (a) To Find: Critical poits. (b) To Sketch: Phase…

Q: Letter C is 59E, not 53E

A: We need to write (59E)twelve in base 10. (It is given that face value of E is 11)

Q: Prove by contraposition that for all integers n, if n is odd, then 5n 4 is odd.

A: We need to prove if n is odd, then 5n - 4 is odd by the method of contraposition.  The…

Q: 4. x. 5. y"+y sin² x.

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Q: 5. Stanley Bank offers a money market account that earns 1.85% compounded continuously: a) If…

A: (a). The formula for continuous compounding is A=Pert, Where, A is the final amount,P is the…

Q: Let T: R³ R³ be the linear transformation defined by T(#1, #2, #3) = (1-2, 2-3, I3 - #₁). Find a…

A: We see,      T(x1 , x2 , x3) = (x1 - x2 , x2 - x3 , x3 - x1)                             = (u, v, w)…

Q: -{] 2. Suppose that X = subspace of R³. € R³ : (x - y) (x − z) = 0 Determine (with justification)…

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Q: Find the weighted adjacency matrix of the following directed graph and represent that as a…

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Q: Direction: Write T if the statement is true and if it is false, underline the word/s that made the…

A: The statements defining and describing the mathematical concepts or definitions or terms used.

Q: 5. Use Green's Theorem to evaluate (x² - y2) dx + (2y-x) dy,where C consists of the boundary of the…

A: Let M=x2-y2 and N=2y-x. We have to compute the integral ∮ x2-y2dx+2y-xdy on the closed curve C. It…

Q: (T 1) (core) Is the following linear transformation injective? Surjective? (Justify both with full…

A: A given transformation T is injective if kernel(T) = {0} (vector)    Here, T(x, y, z) = (x + 3y, y -…

Q: Question-4) √ √√-1+ seca da =?

A: The given problem is to evaluate the given integral of function. Given function √(-1+sec(x)).

Q: Which of the following regions are simply connected? Select all of them. R². A solid triangle in R².…

A: Please find attachment

Q: Consider the autonomous differential equation = P(100P), which could be used dt to model the number…

A: Since you have posted a question with multiple subparts, so we will solve only the first three…

Q: 2. Let K be a field and let ƒ € K be a nonsquare (i.e. there is no element a € K such that f = a²).…

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Q: (c) Let f(x) and g(x) be nonzero polynomials in R[x], of degrees m and n, Prove that deg(f(x) g(x))…

A: According to guidelines we can do only first question thank you. Let f(x) and g(x) be nonzero…

Q: . Find the inverse Laplace transform L¹. L' s² +6s+9 (s-1)(s-2)(s+4) f

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Q: 6. Find the area of the part of the surface z = x²-y², which lies in the first octant that is inside…

A: The solution is given by

Q: 4. Determine the exact equation of the tangent line to the function y = 3-4 cos at x = IT

A: According to the given data, find the tangent line of a function.

Q: 1. Let f: N→ N be a rule defined by n f(n) = 2 if n > 1 2n + 1 ifn ≤ 1 (a) Is f a well-defined…

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Q: Prove: Let fand f' be continuous on [0,0] with both exponential order a. Then, for s>a, L{f}(s) =…

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Q: (a) Find the magnitude of the following vectors. i. u = (1, 10, 0) ii. v = (3, 4, 5) iii. u + v (b)…

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Q: Suppose T is the transformation from R2 to R² that results from a y-shear of 3 followed by a…

A: Let T : R2→R2 be a linear transformation given by rotating vectors through an angle or θ , then the…

Q: Solve the initial value problem (IVP), (2y^2 + 3xy) * (dx + (4xy + 3x^2) * dy = 0), y(1) = -2

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Q: Let -1 4-G A = -16 Find an invertible matrix X and a diagonal matrix D such that X-¹AX = D. X = D =…

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Q: 13 3] Let A== -10 Find two different diagonal matrices D and the corresponding matrix S such that A…

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Q: Apply the eigenvalue method to find a general solution of the given system. Use a computer system or…

A: Introduction: The solution of the system of differential equation is obtained by finding the…

Q: A portion of a function fis shown to the right. At which of the following points (labelled A - F),…

A: Rate of change of a function f as x moves from a to b is given by (f(a)-f(b)/(a-b) or…

Q: Describe the pattern that is found by taking successive derivatives of the function f(x) = cos(3x).…

A: The given function fx=cos3x. We have to find the pattern of the successive derivative and find the…

Q: A9. Explain why the function f: [1, 2] → R,x → f(x) = x² + ¹/ x (x + 1)5 − 1/1/2 attains a maximal…

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Q: Exercise: Find if limit if ite exs of for fax,y) = хуч собу as (x,y) → (0,0) x² + y²

A: The given function fx, y=xy2cosyx2+y2. We have to find the limit at x, y→0, 0.

Q: Can you solve d?

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Q: 3. Solve the differential equation by the undetermined coefficients method: dy/dt +2y=te²t+t²;…

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Q: Prove that: 4 П (3m — 2) = 280 m=1

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Q: #1 find two other pairs of Polar Cook dingtes of the given Point Cooksinate X70 a) (V₁0) (70 and rco…

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Q: Check if the solution is correct. Correct the mistakes

A: The addition rule is not correct.

Q: Use the vectors in the figure at the right to graph the following vector. 3v+u-2w Select the figure…

A: The graph of the vectors u, v, w are given, we have to sketch the equivalent graph of the vector…

Q: Let the invertible function Evaluate f(x) = 3x³+x+3 1 = ["] † ^¹ (2²) dar dx (Hint: You may use the…

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Q: Determine whether ^- [¦ ¦ ¯1]- » - [8]), ~ - (-¹ ¹ ] b W b is in col(A). b is not in col(A).…

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Q: Graph the polar equation below by first selecting the correct symmetry, then selecting the correct…

A: The given polar equation is: r=-7sinθ+7 To Do: graph the polar equation by selecting correct…

Q: The multidimensional random variables fl= (c) Let x := 2 3 1 ,Σ = x1 X2 Y1 Y2 follows N₁(μ, E) where…

A: a) We have to determine all the independent univariate random variables. (b) We have to find the…