Find the Fourier Transforms of the indicated function: f (x) = e-3x for x > 0 and f (x) = e2x for x < 0

Q: Find the general solution of the following PDE. ru +(sin x +y)u+u=2cos2.

A:

Q: variation of parameters to ve the x = 201 0 20x+ 013 H value pro e2t x(0) = =

A:

Q: Topic: Diffusion Equation u_t = aplha * u_xx with conditions: u(0,t) = 0 and u(0,L) = 0 Solve the…

A:

Q: Let V = span{v₁, V₂}, S = {V₁, V₂}. Show that x is in V and find the coordinate vector of x, (x)s.…

A: Let V=spanv1 , v2  ,  S=v1 , v2  Given that the vectors v1=11-5107  , v2=14-81310 , x=19-131815 .

Q: Construct a graph with vertices H, I, J, K, L that has an Euler path, the degree of I is 1 and the…

A: Given that a graph with vertices H,I,J,K,L that has an Euler path, the degree of the vertex I is 1…

Q: The following table gives the percentage of on-time arrivals in airports in a certain country from…

A: We are given the percentage of time intervals data and we are asked to find the mean and standard…

Q: Find the B-matrix for the transformation x+Ax when B = {b₁,b₂, b3}. 43 A = 1 20 -8-88-22 6, b₁ -4…

A:

Q: Let A 1 1 and b=-6. The QR factorization of the matrix A is given by: [21] B = - + √2] X = √2 [0] a)…

A:

Q: 5.) Evaluate the indefinite integral: tan³5x sec²5x dx

A:

Q: 2. Let f: DR where DCR is open, and suppose that f € C²(D). Let xo E D and suppose that B(xo, e) CD…

A: Given that f:D→ℝ, where D⊆ℝn is open and f∈C2D. Let x0∈D. We know that: ∂f∂xix0=limh→0fx0+hei-fx0h.…

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…

A:

Q: Suppose that f(x, y) = x² − xy + y² − 3x + 3y with x² + y² ≤9. 1. Absolute minimum of f(x, y) is 2.…

A: I have explained everything with in the solution .please go through that

Q: Express the solution of the given initial value problem as a sum of two oscillations. Primes denote…

A: The given initial value problem is x''+49x=90cos2t, x0=x'0=0. We have to find the solution to the…

Q: For all parts of this question, suppose f : A→B and g : B→C are functions, and g ◦ f : A → C is a…

A: Functions :f: A→Bg: B→Cf: A→C is a bijection.

Q: Choose the correct adjacency matrix for the following graph. E B a. 12100 0001 020 11 0

A: We have to find the adjacency matrix with the help of graph vertices

Q: 1. Determine the truth value of PAQ and PVQ for each of the following: (a) P is "√-1 is not a real…

A: AND OPERATION: output is True only if both the input values are true, else the output will be false.…

Q: Let a₁, a5 denote the columns of the matrix A, where r5 1 2 2 0 3 3 2 -1 -12 8 4 4 -5 12 L2 1 1 0 -2…

A:

Q: Let f(x) = sin(10x) Find approximate value of the derivative for x =11, h = 0.1 Use forward…

A:

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: Consider the following system. = 7x + y, dx dy dt dt Find the eigenvalues of the coefficient matrix…

A:

Q: 2. A manufacturer sells his notebooks for P41.75 and his cost in producing each notebook is P35.25.…

A: According to guidelines we can do only first question thank you.. We have to find mark up= selling…

Q: A certain experiment produces the data (3,7.5), (4,5.4), and (5,-0.4). Describe the model that…

A: A certain experiment produces the data (3,7.5), (4,5.4), and (5,-0.4). We have to describe the model…

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: Could you do a formal proof of the following: (you may rely on Theorem 4.6.1, that is irrational).…

A:

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

A: Please find attachment

Q: Find the slope using the line perpendicular to y=2x

A: Given that, find the slope using the line perpendicular to y = 2x.

Q: Identify if the following graphs have an Euler Circuit or NOT. Fill in the space provided for each…

A: Definition : Let G be a connected graph. Then G is said to be Eulerian if it contains an Euler…

Q: Find the first three nonzero terms of the power series solution of the initial value problem y" -…

A: The given problem is to find the power series solution of first 3 non zero terms for the given…

Q: Find the National Income if the consumption and Investment are given in th following forms Yt+2 -…

A: Solving the given second order differential equation

Q: (b) Let K be the set of integers with the operation o defined by xoy=x+y + 1. Prove that K with the…

A:

Q: et u and v be vectors in R 3 such that ∥u∥ = 30 and ∥v∥ = 5. What can we best say about |u · v|? (a)…

A: One must verify a few claims, using the rule of dot product.

Q: 6) Let / be a Poincare line and let P be a point not on 1. Drop a perpendicular from P to 1. Let Q…

A: Given l is a Poincare line and a point P not on l. Drop a perpendicular from P to l. Let Q be the…

Q: Find the area of the part of z = 12-x² - y² between z = 3 and z = 8. =

A: For the given part of surface z=12-x2-y2  between z=3 and z=8 To find the area of the part of the…

Q: For all parts of this question, suppose f: A→B and g: B→Care functions, and g ◦ f : A → C is a…

A:

Q: The gradient of f (x, y) = x sin (y²) is the vector field F(x, y) = at (2,√7/6) and ending at…

A: The given scalar function is, f(x,y)=xsiny2. Gradient of this function is F=siny22xycosy2. The…

Q: (b) Compute the radius of convergence of ∞ n=0 (4+3i) ₂2n n + i ∞

A:

Q: What is the surface area of a hyperbolic paraboloid described by parametric eqn: z = xy, where x,…

A: The surface area of a hyperbolic paraboloid described by the parametric equation z = xy, where x = u…

Q: xy² (0) (Use syntax like [3,-4,5] for vectors.) Let F (x, y, z) = xz5 What is the value of curl F at…

A: The vector F(x, y, z) is given. We have to find the value of curl F at (3, 2,1) .

Q: a. || 8 3)++ (-2) x+ t> 0

A:

Q: 7.) Find the area of the region bounded by the graphs of the equation given below. 2 y = (x - 2)²…

A: (.)   Area of the region bounded by the graph of  y=x-22 and  y=4-x2  . Then area is given by ,…

Q: (a) Let f(x, y) = x² + y². Plot the vector field Vf and the level curves of f on the same plot. (b)…

A: A function fx , y=x2+y2. To Find: a) Plot the vector field and the level curve of f. b) Do your…

Q: Which of the following statements are correct for the pde -2uxxx +3vxt-7u, = e sinx Auft A) Linear,…

A: This question  is about  partial  differential equation

Q: a.) [f(x) - 2g(x)] dx 'A b.) [2f(x) dx A c.) [f(x)]² dx A

A: Few results of a particular definite integral are given.

Q: • A quadric surface has the equation x² + 2y² + 2z² + 2yz = 1. Write the equation in standard form.

A: “Since you have posted multiple questions, we will provide the solution only to the first question…

Q: hat value(s) of b can 3 be written as a linear combination of 8 (120)} -2 b

A: For value of b we find when the system have unique value .for this we do the determinant of given…

Q: The gradient of f(x, y) = x sin (y²) is the vector field F (x, y) = at (2,√π/6) and ending at…

A: Here we are given that the gradient of f(x,y)=xsin(y2) is the vector field F(x,y)=sin(y2)2xycos(y2)

Q: 1. Solve the difference equations and analyze the time paths Yt+22yt+1 + 2yt = 1, Yo = 3, Y₁ = 4

A:

Q: At Hartford College, Lateefah obtains experimental data for the rate of change of f(a). The graph of…

A:

Q: Find the surface area of that part of the sphere x² + y² + ² = 81 that lies outside the cylinder x²…

A: