H.W. 1. Find the Fourier transform of f(x) Hence prove that fo dx = sin² x x² :=/ = Sa- |x|, |x|

Q: Find the volume of the solid whose base is the circle x² + y² = 49 and the cross sections…

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Q: Are the following functions odd, even, neither odd nor even (a) x² cos x (b)sin x +cos x (c)f(x)=ex²…

A: According to guidelines i solve first 3 subparts of first question only. So kindly request you to…

Q: O f(t)=e-1t (cos(4 t)- 10 sin(4 t))

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Q: Find the equation of the parabola that passes through the given set of points. (-2,1), (2,-7),…

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Q: Working directly from the definition (not using Arithmetic of Limits or any other results proved in…

A: Given fx=x2 To prove: limx→3  x2 =9.

Q: 4. (a) Let f: X→Y, g: Y→ Z, and h: Y→ Z be functions. Prove or disprove: If gof=hof, then g = h. (b)…

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Q: Find the general solution of the given system. dx dt dy dt (x(t), y(t)) = = 4x + y = -2x + 2y e³t C₁…

A: Note: As per our Guidelines we can solve first question.Please repost remaining questions.

Q: 45 If y=1+ 2 a3x² a ₁ (x-a₁) a₁) (x − a₂) (x −a3) [.. X X a2x (x-a₁) (x − a₂) +... to (n+1) terms, s…

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Q: dy dx = 35 Ify= = 1+ 1+ sin x COS X sin x 1+cos x ... (1 + y) cos x + sin x 1+ 2y + cos x - sin x 9…

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Q: 44 if x = 0 [cost += log tan²t) a dy П and y = a sint, then find at t == dx 4

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Q: To find a particular solution for y" - 6y' + 9y = x² + 10 with the method of variation of…

A: The given differential equation is a second order non-homogeneous differential equation with the…

Q: +1 If p is a natural number, then prove that pn +¹ + (p + 1)²n-¹ is divisible by p²+p+ 1 for every…

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Q: Find the eigenvalues of the matrix A ii) Find the dimensions of the eigenspaces of the matrix A.

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Q: Use the divergence theorem to calculate the flux of the vector field F(x, y, z) = x³i + y³j+z³k out…

A: Given : F→x, y, z=x3i+y3j+z3k x2+y2≤4, 0≤z≤3 To find: ∬S F→ ·dA→

Q: Suppose F(x, y, z) = (x, y, 5z). Let W be the solid bounded by the paraboloid z = x² + y² and the…

A: F→x,y,z=x,y,5z The solid is bounded by the paraboloid z=x2+y2, z=25

Q: The augmented matrix is given for a system of equations. If the system is consistent, find the…

A: We are given an augmented matrix for some system of equations. Our aim is to choose the correct…

Q: Consider the following initial-value problem. -1 -2 *'- (-3-²)* +(²). ×(0) - (-3) X' = 4 Find the…

A: We solve the initial value problem.

Q: II. Let S be the portion of the cylinder x² - 6x + z = 4, oriented by upward-slanting normal…

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Q: The Palermo scale value of any object can be found using the equation PS= log₁0 R, where R is the…

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Q: 1² + 1 1-2r sin ¹(t) + x² 2. Find the equation of the tangent line to the graph of F(2) = ₁2 s dt at…

A: Equation of the tangent line to the curves

Q: 12. Let : G→ H be a group homomorphism. suppose that K is a normal subgroup of G. Prove or disprove:…

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Q: Problem III Let A denote the matrix given below. (i) Find all eigenvalues of the matrix A. (ii) For…

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Q: Let L be the line segment with endpoints at (1,2,3) and (-1,1,4). A light source at is at the point…

A: We will find shadow of given points on the plane given and then find parametric equation of the line…

Q: 3. (a) Let f: X → Y and g: Y→ Z be functions. Prove the following statements. If f and g are both…

A: We can prove the following parts .

Q: 4. Let A = [¹]. Show that A can be diagonalised.

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Q: Consider the complex number z given below in rectangular form, and marked on the complex coordinate…

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Q: Write the following arguments in symbolic form and test for validity using truth tables. If an…

A: Given an argument, if an animal is a rat then it is 4-legged. If an animal is a human then it is not…

Q: Use the row reduction algorithm to transform the matrix into echelon form or reduced echelon form as…

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Q: Prove or disprove. Let A, B and C be sets. If AxC=Bx C, then A B

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Q: 2. Solve the Ordinary Differential Equations (ODE) by the Series method. (x²-x)y"-xy'+y=0

A: The given ordinary differential equation is x2-xy''-xy'+y=0. The objective is to calculate the…

Q: From the 7 choices, select all that apply span{ |} + { 1 C -4 } span{ span{ span{ 1 O {0} 1 -1}+{0}…

A: Subspace must contains zero vector with respect to addition. Affine subspace is not consider here.…

Q: A glass sphere given by the equation (x-1)²+(y-2)²+(-3)² = 36 is floating above the plane 2x + y -…

A: The given problem is to find the point on given sphere is farthest from the given plane. Given…

Q: Match the equations with the graph descriptions. ⠀⠀ y = log (x-2) + 3 y=-In(x + 3) - 2 y = log(x +…

A: TRANSFORMATION OF FUNCTIONS-: IF WE HAVE AN FUNCTION y=f(x),THEN (1) f(x)+k MEANS A VERTICAL…

Q: Problem F.1 where x > a, a constant. Use any method to find the GS: 2 y"" (x − a)² y' 1 (x − a)³

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Q: Find the indicated number of elements by referring to the table of enrollments in finite math class.…

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Q: A confectioner sells two types of nut mixtures. The standard-mixture package contains 100 g of…

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Q: If s, is the arc length of locus of centre of curvature, then show that √√k²q² +k¹². k² ds, ds (e)…

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Q: Find the equation of the plane containing the line 2+²=1,x=0_ 0. b с

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Q: Question 29 Solve the system of equations. x1 + 3x2 + 2x3 = 11 4x2 + 9x3 = -12 x3 = -4 O (1, -4, 6)…

A: The given problem is to find the solution for the given system of linear equations.

Q: our team is preparing a variety of pastries for a brunch event this weekend. You anticipate that…

A: 25%of the pastries will have 2 ounces of lemon filling.  Anticipate that each of the 400 guests will…

Q: Find the solution of the following equations using the Jacobi and Gauss Seidel iteration method…

A: Question (b) using gauss seidel method asked and answered.

Q: Consider the function 0 if -3≤ x < -1, 1 if -1<x< 1, 0 if 1 ≤ r < 3; a) Sketch the graph of f on the…

A: (a)

Q: Let A be a nonempty set and B be a fixed subset of A. Define R to be the relation on P(A) such that…

A: Given information A non empty set A and B is a fixed subset of  A. Power set of  A :- PA Relation R…

Q: Given the graph below, solve the following inequality: k(t) > 0 110|1) 9 8 -10-9-8-7-6-5-4-3 N 7 16…

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Q: 2 - i)₁ dz, 4 dz, r = {2: 2-1 - i| =

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Q: Semi transverse axis of hyperbola is 5. Tangent at point P and normal to this tangent meet conjugate…

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Q: Question 30 Calculate the flow or line integral in the field F along the path C. F = y²i+ + zj + xk;…

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Q: Provide detailed steps for this nonlinear system of equations X^2+y^2-6y=0 4x^2+5y+20y=0

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Q: First four steps of step 2 (in general entire step 2) is not clear. Request clarify in easier to…

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Q: 19) If f/u) = sinul; then (fog)(3) = ? A) O B) 1 M= g(x)=x²-9₂ c) 6 D) 9 E) None

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