Šolid bounded by yzo, xty=2 とこの in first octant write a tiple integral in cylindrical coordinates (dxdrd o) and soluve

Q: Evaluate f (z) = Vz + cos² z_from -0.4 to 2 using Simpson's % rule. with eight segments. Round off…

A: Given: f(x)=x+cos2x3 Interval=-0.4 to 2

Q: Find the solution. (D2-4D +7)y = 0 y = e-2(c,cos3x +c,sin3«) Oy= e"(c,cos/Zx+c,sin/2x) O y-…

A: Given differential equation is (D2-4D+7)y = 0

Q: (2n )! | [P, (x)]° dx | (1-x?)" dx %3D 22" (n!)2 -1

A: Solution

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Q: Compute the Fourier Transform of f(x) = e-ax-

A: Fourier transform of a function fx is defined as  Ffx=∫-∞∞fxeisx dx Gamma function =∫0∞e-x xn-1 dx

Q: Find a basis among the vectors [1,1, 3]; [–1,0, 10]; [0, –3, –2]; [–1, –3, –5] (which are surely…

A: Here we are given 4 vectors in ℝ3, which are:1, 1, 3; [-1, 0, 10]; [0, -3, -2] and [-1, -3, -5]To…

Q: if j = 1     the expression is x if j = 2     the expression is kx + x if j = 3     the expression…

A: if j = 1     the expression is x if j = 2     the expression is kx + x if j = 3     the expression…

Q: What is the general solution to the differential equation y- (9 - + = 0 ? dx In(Ay – 2) = Ax +B y2 =…

A: We have given a differential equation ,  yd2ydx2 - dydx2 + dydx = 0 This can be written as ,  y y''…

Q: For x,y E [0,1], prove that xy(1-x-y)≤1/27

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Q: ()* + dy What is the general solution to the differential equation y = 0 ? dx In(1+ Ay) = Ax + B y2…

A: We have yd2ydx2-dydx2+dydx=0 Let dydx=p Then d2ydx2=pdpdy So, yd2ydx2-dydx2+dydx=0 becomes:…

Q: Using MOSA find the polynomlals that will approxlmate the solution to: y'= x2 + y; y(1)-1. y1(x). A…

A: y'=x2+y;    y(1)=1 f(x,y)=x2+y;    y0=1

Q: Question 8 Consider the following IVP: x" - 4x' + 4x = 4e2t; x(0) = -1, x'(0) = -4 Find the general…

A: Given is an IVP with initial conditions   To Find:  Solution to given IVP with initial conditions…

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Q: 2 The series 3 32 128 +. 7.י3 is equal to 33.3 35.5 +

A: Given series is 23 - 833·3 + 3235·5 - 12837·7 + . . .

Q: Find the Laplace Transform of f(t) = cos? 3t (A F (s) 2 2+ 36 s 1 B F(s) s2+ 36 6 (c) F(s) = - s2+…

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Q: 6. Tell whether the series whose nth term is given below converges absolutely, condition- ally, or…

A: Please post the multiple parts separately. Here I answered 1st question as per our policy.

Q: 2. The linear differential equation x*dy+(2y-3x²y-x' dx 0 has the integrating factor equal to (Note:…

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Q: Solve: y'' + 2y' – 15y = – 45t – 84 y(0) = 9, y'(0) = 28 y(t) =

A: We have to solve the given problem.

Q: 2xージ f (x) : 33 Vx2 T sin 2x + Ve2x + 2x –- In e, x # 1 1-x (1–3t)5(t³-8) g(t). t # 2 2-t

A:

Q: What is the particular solution to the differential equation * + (1 + x)y = 12 with y 0 and = 0 when…

A: The solution is given as

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A: This is a problem of function.

Q: Tests for Convergence 1. Consider the series Inn n=1 a. Use Comparison test to show that the series…

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Q: What is the particular solution to the differential equation dx 1 + y = 2e-* with y = 1, dy -1 when…

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Q: (2n)! Σ (2n)!

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Q: 31. Let R* have the Euclidean inner product. Use the Gram- Schmidt process to transform the basis…

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Q: You want to receive ​$400 at the end of every six months for 5 years. Interest is 11.8% compounded…

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Q: Solve the given system of linear equations using the Elimination Method. 4.)     2x1 + 7x2 + 15x3 =…

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Q: ) Using the same universal set, find the set specified by each of these bit strings. (i) 11 1100…

A: It is given that U=1, 2, 3, 4, 5, 6, 7, 8, 9, 10. We have to write the elements of the set specified…

Q: (1+t2) ds + 2t[st2 – 3 (1+12) ²]dt = 0; when t = 0, s = 2.

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Q: Show that the lines L:a =4- t, y = 2t, z =1+t and L2:2 =1+ 21, y = 3 – 4t, z = 5 – 2t are parallel…

A: This is a problem of 3D analytical geometry and application of calculus, vector calculus.

Q: Let C be the parametric curve defined by (x(t) = t2 – t – 2, 1 y(t) = t³ – t² + t. Determine if C is…

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Q: Consider the following IVP: y"- y = 4cos t; y(0) = 0, y'(0) = 1 Find the general solution. A y(t) =…

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Q: The object shown in the figure is axially symmetric and its curved surface is described in…

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Q: dy dx ytsinx I+ CoS X

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Q: х — 3 2. Graph the function f(x) = Identify asymptotes and holes in the х2 — 4х + 3 graph. Answer:…

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Q: Find an isomorphism from the group G = to the multiplicative group {1, i, – 1, – i} in Example 3 of…

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Q: b) Given a linear system as below х — 2у + 3z %3 9, —х + Зу %3D — 4, 2х — 5у + 5z %3D 17 Find the…

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Q: Q6. Use the method of Variation of parameters to solve (i) y" + y = tan x. (ii) x²u"+xy' +(x² – !)u…

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Q: Which of the following is the general solution to the differential equation x + (1 +x)y = 6? dx xy =…

A: The solution is given as

Q: Relationship Y= (ax+bX) - Find the Linearizationof Nonlinear

A: This is the problem of application of differentiation.

Q: 3. Use zero- through third-order Taylor series expansions to predict f(3) for f(x) = 25x³ 6x2 + 7x –…

A: Given below clear explanation

Q: When the insured knows more about their circumstances than the insurer, there is O propitious…

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Q: 3. Determination of integrating factors: 2y(x+ y+2)dx+(y² –x² - 4x -1dy = 0 4. Substitution…

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Q: Prove each of the following by mathematical induction. 1.3 + 2.4 + 3.5 + ..+ n (n + 2) = (n) (n+1)…

A: The Principal of Mathematical Induction states that if P(n) is defined for integers n, and a fixed…

Q: Determine whether the given series is convergent or divergent. 5" + sin? n a. Σ 3" - | sin n| 7 b. E…

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Q: 2 Mrs. Rogan is a Mathematical teacher -she gives a 60-item test The scores OF e 46,…

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Q: 2) If we know that y,(x) = e2* is the solution for the equation (2) xy" + (2x – 1)y' – 2y = 0 (2) a)…

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Q: (D4 + 6D3 + 9D?)y = 0 Ay = (c,+c)x+(c3+cx)e* , 3x y = c,+c,x+(cz+c,)e* y = c,+c*+ -3x D +

A: Given differential equation is (D4+6D3+9D2)y = 0

Q: Find the solution. (D* + 1802 + 81)y = 0 Ay = (c, + c,)cosår + (cz+c,)sin3r. ® y = (c, + cx)cos3r +…

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Q: 12. In a standard deck of 52 cards, each card has a suit and a rank. A, hearts ♡, clubs , and…

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