If the Wronskian of the DE : x³y' +xp(x)y' + 3y = 0 is μ (x) ee Find p(x) = 2r er? -2 -2x 2x4 2x 2x3 2 r3

Q: x  ≤  12 −4x + 144 x  >  12 Evalute 36 ∫ 0 f (x) dx. (Note that since  f (x) is defined in a…

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Q: Find fryz from the functions f(x, y, z) = 4x³y² – e²y* ++ 4y – x16 %3D - |

A: To find the third order partial derivative of the function fxyz f(x,y,z)=4x3y2-ezy4+z3x2+4y-x16

Q: ind the following Non homogenous LDE using Reduction Order. (D² – 4D + 4)y = e*

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Q: What is the linear approximation of this function at (1,0) F(x, y) = (F(x, y) = (x² cos(x+y)) x²y 0…

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Q: The critical Points of f(x, y) = x3 – 3x + 3y? – 6y are: None of these O (1,-1) and (1,1) O (-1,1)…

A: Partially differentiate with respect to X and Y and equate with zero. Solve both equation and get…

Q: 1 Integrate with respect to x. 4+ 25(3x +1)²

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Q: Let y1 = 9cos(2x) and y2 = 2cos2 (x) – 2sin? (x). Calculate the Wronskian, W(y1, Y2). Give your…

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Q: An agent makes decisions using U(ct) = {[ct−χc(t−1)]^(1−γ)} /(1−γ) . Answer the following: (a)…

A: (a) When , the utility function becomes . To derive the expression for the coefficient of relative…

Q: Find the linearization L(x) of f(x) at x = a. f(x)=x+, a= 2 3 O A. L(x)=x+1 3 2 23 OB. L(x)= x+3 5…

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Q: dx 2. Evaluate 1 (1+x²)+√1+x6 by Composite Simpson's 1/3 Rule..n=4 n-1 f(xo) + 4 Σ1,3,5... f (x;) +…

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Q: If the Wronskian of the three functions ex v is equal to zero, then the function y satisfies the DE…

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Q: Show f(x) = e2= and g(x) = x e²z linearly independent by finding its Wronskian.

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Q: Let f, g:R R defined by if x 1 (x2 and g(x) = 3x + 2. %3D Find f-1 and g-1.

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Q: S(x) Q:1) a) If f(x) = /1- x and g(x) = then find the domain of g(x)' b) If f(x) = x – 3, g(x) = vã…

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Q: 4) Let g(x, y) = x³ - 3xy - 6y. a. Evaluate Vg b. Evaluate 9xy Find the critical point(s) of g.

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Q: If f(x)=e4x+6, the linear approximation L(x) of f(x) at x=In(4) is OL(x)=e6(1+44(x+In(4)))…

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Q: 4. Find the critical values of Z = 12x2 – 18x - 8xy - 26y + 9y2 + 40 and check whether the equation…

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Q: Let f(x) = (2- . 2x) and g(x) = 8x + 1. %3D Find g(f(x)). 08(2³ 0 8(2° – 2x)' +1 O (8x + 1) - 2(8r…

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Q: 3. Integrate f 10(x+6) x² + 3x-10 2 dx by using partial fraction.

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Q: Let f(x) = {x²ca-1), Sx²e2cx-1), lacos(2x - 2) + bx? x>1 f(x) will be differentiable at x = 1, if…

A: We have to solve given problem:

Q: C. f(x)=x³ (4-x)

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Q: 4. Let f(x, y, z) = e²x + √y-2², with x = rsinh ¹(st), y = 38²4-¹ and af by using the chain rule.…

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Q: ) Given y = f(x) and xo = 1, x₁ = 3, x2,= 7.Compute Lagrange multiplier Lo for the data.

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Q: In FDM, the second order ODE with BVP needs to be written in general form y" + p(x)y' + q(x)y=r(x).…

A: Option(c) is true

Q: a) Calculate [6x² (1-y) 0<x<1 0<y<1 0 otherwise b) Evaluate £xv (x, y) = {6x*(1-y) fxy…

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Q: x²-32 12-R Let f(x) = g(x) = 6x5 – (3R + Z) , h(m) and k-'(10 – 3x) + R+2x m2 3x = 4x, then find: a.…

A: "Since you have posted a question with multiple sub-parts, we will solve the first three sub-parts…

Q: Let f(x) = cos ¹x for -1 ≤ x ≤ 1 ( the principal branch 0 ≤ f ≤). Find the polynomial of degree 2,…

A: Given Information:Function is given as  for .Integral To find:The polynomial  of degree 2, in which…

Q: 2. (a) (b) Consider f(x) = 10 (x − 1)(x² + 9) Decompose f(x) = = dx. 10 (x − 1)(x² +9) more space,…

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Fundamentals of Trigonometric Identities

Trigonometric Identities are the equalities that involve trigonometry functions and hold for all the values of variables given in the equation.