Q11) Determine if 8 (t) and 8' (t) even or odd by utilizing properties of Fourier transforms. What are the value of 8 (1) dt and 8' (t) dt?

Q: The general solution for the linear homogeneous system depends only on the free variables and there…

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Q: Let FC be the splitting field of x² -2 over and ==e7 Let [F: (=)] = a[F: (√2)] = b then? a) a = b =…

A: Option a is correct i.e. a=b=7.

Q: Let C, D and E be the polar curies below: Cir=f(0) = 3-3 cos 0 E³r = g(0) = 1/2 500 € C D: r = 3 the…

A: (1)C : r =f(θ) =3-3cosθ,E : r =g(θ) = 32secθSo,C0 : r =f(θ) + g(θ) =3-3cosθ +32secθ⇒r =3-3cosθ…

Q: f(x) = 3 - 2x and g(x) = ln (x - 1) then (image attached) = 1. -2 2. None of these 3. 3 4. 1

A: Composite rule is used

Q: (i) At x = 1, the Fourier Series of f(x) = converges to: (A) 0 (B) 1 (2-2x, -1<x<0 0< x≤1 (C) 2 (D)…

A: At x=1 , the function value is 0. i.e. f(1)=0 Therefore, at x=1, the Fourier series for f(x)…

Q: 2. Using both trapezoidal and Simpson rule, find the approximate values for the integral In(tan…

A: We need to find the approximate values of ∫π4π2ln(tan(x))dx using trapezoidal and Simpson rule given…

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Q: 2. Show that if the orthogonal dimension of a Hilbert space H is finite, it equals the dimension of…

A: Given: Finite dimension To find: Former finite

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A: we are given a solid and we need to find The Centroid or center of mass.   About the solid in…

Q: Find the orthogonal matrix and upper triangular matrix in matrix A using QR method.

A: Solution

Q: Consider the initial value problem u" + p(t)u' + q(t)u = g(t), u(0) = uo, u'(0) = u Transform this…

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Q: 2. Using both trapezoidal and Simpson rule, find the approximate values for the integral…

A: Let  I= ∫π4π2ln(tanx)dx Here, a=π4 , b=π2 , f(x) =ln(tanx) Step size h=b-1n=π2-π410=π410=π40 Then…

Q: Evaluate be (x² + y²) ds, C is the right half of the circle with radius 3 centered at (0,0). Hint:…

A: Solution:-

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A: The minimum possible order of a homogeneous linear ordinary differential equation with real constant…

Q: answer letter b

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Q: The gradient of the tangent to the curve (image attached)   at  x = 2  is  4. The value of  a  is…

A: The gradient or the slope of the tangent to the curve: y=fx at x=a is f'a.  It is known that…

Q: Let S be the surface with equation 4y2 + 4z²x² - 16 -0. 1. Find an equation of the trace of S on…

A: Solution:S be the surface with equation 4y2+4z2-x2-16=0⇒4y2+4z2-x2=161)Traces of S in the coordinate…

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Q: The marginal cost of manufacturing a certain product is dC/dX = 17 + 0.005x .  If the cost of…

A: Solution

Q: III. Let S be the quadric with equation 4x² − (y - 3)² + 4z² = 4. a. What type of quadric is S? Find…

A: Let S be the quadric with equation    4x2 - (y-3)2 + 4z2 = 4 ⇒x2 - (y-3)2/4 + z2 =1

Q: Q3: Use finite difference method to solve Laplace equation in the red (hand written plzzz) domain…

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Q: The total area bounded by the curve y = f(x) and the x- axis on the interval [-3, 3], which area…

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Q: Given the periodic function defined in one period by the function: (bt, f(t) = a, (0, 0 0.

A: The following formulae are used to find the Fourier coefficients of the function fx on the interval…

Q: Given: planes II₁: 2x - 5y + z = -1 and II₂ : x + 5y + z = 5 intersecting on a line l (a) Compute…

A: Given: Planes π1:2x-5y+z=-1 and π2:x+5y+z=5 intersecting on a line l.

Q: Consider a curve given by Ř(t) = (2 cos t, 12t + 3, -2 sin t). Let f(t) be a function such that f(1)…

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Q: 1-x 2+3 Consider the point P(1,-1, -3), the vector u = (2, 1, 0) and the line l : = y + 1 = 3 2…

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Q: y = −2x4 + 4ax³ - 5x² - 8x + 1

A: Solution:-

Q: Using Pappus Theorem, find the volume formed by revolving about the x-axis the area bounded in the…

A: Consider the given parabolas, 2cy-x2=0 and x2-4cy=c2 The graph of the curves in the first quadrant…

Q: A. SOLUTION OF NON-HOMOGENEOUS SYSTEM GIVEN: 7-3 4 0 0 -7] A = 2 1 -1 14 6 010-3-5

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Q: a 1 - x²) cos(nx) dx F(x 一九 4 sin(nл) — 4nл соs(nл) — 2n²л² sin(n) πη3

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Q: 6. Let x#0 and y‡0. (a) If x 1 y, show that {x, y} is a linearly independ- ent set. (b) Extend the…

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Q: Determine whether each pair of solids is similar, congruent, or neither. If the solids are similar,…

A: The solids represent cones. These are similar if the ratio of their dimensions are equal.  So, we…

Q: 8 (1) = {(In(3-1) 141-13, 38²2-8), t), ‚31² t (0,−1, 4), t . Find the domain of Ř.

A: This is a problem of vector calculus.

Q: please could someone solve this for x -415000 =8.314* 1073* ln x

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Q: 3. ( ) Consider the function f(x) = 4x-8 x+2' a) Determine the key features of the function: i)…

A: As per our policy, we are allowed to attempt only first 3 part of the question. Kindly post…

Q: denotes the set of subsp

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Q: x² A quadric surface is defined by the equation: + 3y² = 3 + z 3 1. Solve the equation of the traces…

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Q: x = -ln(t + 1); y = sint € [0,1]

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Q: Let {f1, f2, f3} be the dual basis of {e1, €2, €3} for R³, where e₁ = (1, 1, 1), €₂=(1,1,−1), Find…

A: Given basis are e1,e2,e3 of R3 where e1=1,1,1e2=1,1,-1e3=1,-1,-1 Its dual basis are f1,f2,f3 We have…

Q: Finding the Determinants using Elementary Row Operations E = 2 1 3 1 10 11 0210 0 1 23 1 1 -2 -7 0 1…

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Q: Find a power series representation for the function 8 using summation 2x-15 sign, determine the…

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Q: Consider the vector-valued function R (t) = ( 8/3 t 3− t, 2t2 , 2 − 2t2 ) - Find II R(t) II…

A: We are given R(t)=(83t3− t, 2t2, 2 − 2t2) to find II R(t) II and distance traveled by a particle…

Q: พ 6

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Q: T b) Evaluate sin530 de (Take n=7).

A: We need to evaluate numerical integral ,  ∫0π2 sin53θdθ   Here , n = 7 We will use  Trapezoidal rule…

Q: Solve the nonhomogeneous system ty' = 3-2 2 -2 Y + -2t ¹-1

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Q: Determine if the function g: RR defined as is analytical og if yes, find its Taylor series. g(x) =…

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Q: Polar curves C1: r = 2 cos 0 and C2: r = 2cos 30 and let R (shaded region). 2π The Cartesian…

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Q: C. MATRIX INVERSION GIVEN: 214 1 13 331 A = 2205 5124

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Q: rector spaces over a field I and t: V--V' be a linear transformation and to be the dual map of t,…

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Q: Which of the following intervals can be an interval of existence of the solution of the linear…

A: x-12y'-11y = x-113 x-12y' = x-113+11y