Find a parametrization, using cos (t) and sin(t), of the following curve: The intersection of the plane y = 6 with the sphere x? + y + z? = 72

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Q: 2. lim E1 5i 4+ 72 A. Vĩ dx B. VA + x dx C. Vã dx D. V4 +x dx

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Q: ン Frnd in side r=2 inford quarler aren aul sde r= 1+s6

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Q: Question 4 Consider the function (a) State the domain of f(r, v). f(I, v) 3zy (b) Find the limit by…

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Q: Q5) Find volume of body bounded by z = 0 from below and z = 4 -x from above inside x = y2,x = 4.

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Q: 9. Solve the following initial-value problem using Laplace transforms. y" – y – 2y = 5 sin(a); y(0)…

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Q: 6. Let y = 9 , U1 , U2 1 |3| L10] 1 Compute the orthogonal projection of y onto W = Span{u1, u2}.…

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Q: Question 36 Consider the quadr atic form f (æ1, 22, x3) = x² + æ3 + 7æž + 22a1æ2. %3D (i) The…

A: Given fx1,x2,x3=x12+x22+7x32+22x1x2

Q: 1.5 (3-x Q1) Evaluate the integral dy dx using polar coordinate

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Q: I. Evaluate the following integrals. 1 1. d.x * ¤(9 – In? x)5/2 -

A: We can solve this using substitution method

Q: Q1) Evaluate the integral dy dx using polar coordinate

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Q: * /In(n), cos?n COS n2 n=| Identify if it converges or diverges

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Q: Reading Question 4.1.3. Which of the following maps is a group homomorphism? (Select all that…

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Q: Estimate the error in using the partial sum of 65 terms of the series k=1 Error DII * @ # $ & 2 4 5…

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Q: QI) Evaluate the integral dy dx using polar coordinate

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Q: salvepE tany= Sin(2 +y) +Sin(x-y) (ans. secy= C-2 Casx)

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Q: 3. State the final value theorem. Verify theorem for the function 4+ e -2t (sin t + cos t)cm…

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Q: Let T be the linear transformation defined by T(x1, x2, x3, x4) : = x1 + 6x2 – 7x4. Find its…

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Q: Find the matrix M of the linear transformation T : R² → R² given by -8x1 + 9x2 5x1 – x2 x1 X2 M =

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Q: Q2) Solve the D.E dy + (xy-xy2)dx 0 %3D

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Q: Problem 6: Consider the following minimisation problem: min subject to (P.) 6(11 – 10)2 + 4(z2 -…

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Q: Consider the system of equations da = x(3 – x – 4y) dt dy = y(1 – 3æ), dt taking (x, y) > 0. Recall…

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Q: 3Fita secand order polynomial bo the dafa in the table below X 1 2. 18 27

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Q: (iii) If u = 461 + 362 and [u]c = then the value of r is and the value of S is (iv) If V = 3c1 + 2c2…

A: Given that  b1 = 10c1 +3c2,  b2 =27c1 +8c2 c1 =-8b1 +3b2,   c2=27b1 -10b2

Q: in Let an n> 1. In(2" + 1)' 1. Determine if the sequence {an}n=1 is convergent or divergent. 2.…

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Q: engineer, and a teacher, not in the same order. They also have Daniel, Bobby, 14. There are three…

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Q: Find the Maclaurin series for the function f(x) = X COS X.

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Q: 3)Solve D-E リラ=メジ (ans.jole) .

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Q: The polygon shown is concave.

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Q: -4 7 + 7 7 -4 7

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Q: 4. A cone just fits inside a cylinder with a diameter of 8 m and a height of 11 m. What is the…

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Q: (FAB 4) Use Lagrange Multipliers to find the maximum and minimum values of f (x, y) = 81x² +…

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Q: Consider the system of equations #--(1--) da dt *= (1 ---). dy dt 3 taking (2, y) > 0. (a) Write an…

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Q: Find the special solution to the following partial differential equation: (D+ D'- 1)(D + 2D'-3) = 4…

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Q: et Determine if the improper integral dx converges or diverges. (1 - e)2 If it converges, find its…

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Q: to find a Use the method of frobenius solution of the fallowing DDE: near

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Q: Determine the curl of the vector field A = pz sin o ap + 3pz cos o ao at (5, ,1)

A: Here we have given the vector field A=ρzsinϕaρ+3ρz2cosϕaϕ. it is required to find the curl of the…

Q: Let T be the linear transformation defined by T(а, у) — (5а + 8y, у, — 4aх — 2у, — 6ӕ — Зу). Find…

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