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

Q: 1.1 Show that if |z| < 1. then lim z" = 0. %3D 1.2 Show that lim Vn = 1.

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Q: Let A be a 2 x 2 symmetric matrix satisfying A = 12 and 3 with the spectral decomposition le A = 12…

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Q: [1] Construct a 2 × 2 symmetric matrix A such that A 3 and -2] -2 8 a11 012 If A = a21 then the…

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Q: Q3) Evaluate triple integral ,a * dz dx dy.

A: Evaluation of the triple integral

Q: 1.Does it follow that if an > 0 for all ne N, thenEn=1 an does not converge conditionally? Explain.…

A: We have to explain the given statement.

Q: 2. Find the characteristic equation, the eigenvalues, and bases for the eigenspaces of the matrix.

A: We have to find the characteristics equation eigen values and eigenspaces of given matrix.

Q: Solve. S1 for 0 5 y" – 3y' + 2y y(0) = y' (0) = 0 The solution can be written as y(t) = f(t)u9(t) –…

A: The solution is given as

Q: Consider the quadr atic form f (x1, 22, æ3) = x} + æ% +7æ% + 22x1æ2. (i) The maximum value of f(x)…

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Q: x′ = xy y′ = x + y2 - 4 What is the shape of the nullclines of the system and how many equilibrium…

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Q: You are given that B = {1 – x², 1+ x, 2x + 3x²} is a basis for P2 and - 2 [p(x)]B= |3. If p(x) = a +…

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Q: 1 2 -2 76. 1 0 -2 3 01 2 2 -4 10 8 0 1 0 2 0 1.A= 0 1 0 2 2 =B 0 0 0 0 1 -2 2 4 -2 6 0 0 0 0 0 a. Is…

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Q: 3. 37 Consider the orthogonal basis B = -3 10 of R3. 3 1 5 Let v = -64 15 a If vB =|b|, what is the…

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Q: Question 2 Find the inverse Laplace transform of -4s H(s) = - e

A: The solution is given as

Q: 8. 1 3 7 k 4 Let A = If the dimension of the eigenspace corresponding 8 5 3 to eigenvalue 8 is 2,…

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Q: 5. Use the method of Lagrange multipliers to minimize f (x, y) = x2 + y? subject to 2x + 8y 102.…

A: The given question is related with Lagrange multipliers . We have to minimize fx , y = x2 + y2…

Q: 2 cVy Q3) Evaluate triple integral N S dz dx dy. x-y

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Q: Question 13 Let T : R? → R*be defined by 1. 8 T X2] x2] .2 If B = is a basis for R´such that T B is…

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Q: Find a power series representation for x2cos(2x) and then by differentiation, show tat the equation…

A: Power series exaption of the function

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: d'N Solve t? dN -21- -+2N t Int di? dt

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Q: Determine whether the following series converges or diverges

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Q: Gniert y=x to polor to polar ニ 22 と= tane to Cortesian r Sinl a 色) ta Gatssian

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Q: Question 17 Suppose that is an eigenvector of a matrix A with corresponding eigenvalue ó. Then x is…

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Q: 2. Use the met hod of undet er mined coefficients to solve t he syst em x' = Ax+f, where b. A = f(t)…

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Q: Recall that e* : o! for all x ER n: 0 (1.) Find the Maclaurin series for xe * (2) Use the 2nd de…

A: We have to find the maclaurin series for xe-x

Q: t and W = Span -2 For what value of t is Let U = 1 3 the vector U orthogonal to W ?

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Q: Using polor Codirote to Sad ared bourded buu ブニ4 1ノ=ル /

A: Area along the xy plane , conversion of polar coordinates

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

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Q: The center of pressure on a sail is the point (ap, Yp) at which the total aerodynamic force may be…

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Q: You are given the data points (xi, Yi) for i = 1, 2, 3 : (2, 3), (1, –8), (2, 9). If y = a + Bx is…

A: We have to apply the least squares method to solve the problem.

Q: Find the surface areas of the figures on the right. (a) The surface area of the right trapezoidal…

A: Given the right trapezoidal , we are to find the surface area of the trapezoidal.

Q: 8. 1 3 5 k Let A If the dimension of the eigenspace corresponding 0 0 8 5 0 3 to eigenvalue 8 is 2,…

A: We have A=813705k400850003 Now for eigenvalue 8 we find the eigenspace. Consider:…

Q: Question 11 8. 1 3 7 k 4 Let A = . If the dimension of the eigenspace corresponding 8. 0 0 0 3 to…

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Q: Question 28 Consider the inner product space (P2, (,)) with the inner product (p(t), q(t)) =…

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Q: What is the solution of D.E (D² – 2D)y = e* sinx when solved using the method of undetermined y = C1…

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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: QI) Evaluate the integral dy dx using polar coordinate

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Q: Solve D. E y %3D

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Q: Question 2 3 Cansider the arthagonal basis B: of R 5 Let U = -64 15 If [v]B = 6|. what is the value…

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Q: You are given that B = {1+2x², 1 + 2 + 3z,-8z- 5z²} is a basis [5 for P2 and p(x)]B =4.f p(¤) = a+…

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Q: Question 34. Let A be a symmetric matrix. Suppose that u and v are two eigenvectors of A…

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Q: [4 1 1 1] 4 1 1 You are given that the eigenvalues of A = 1 1 are 1 4 1 1 1 1 4 7,3, 3, 3, counting…

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Q: 1? d²N dN – 2t-+ 2N =t ln t dt 2 di?

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Q: what is Selution of DE (D-20)Y=ê Sinx When Sotved using the meth ed of undetermind

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Q: 1 0 2 Is X = 2 an eigenvalue of 3 1 -4 ? If so, find one corresponding eigenvector. -2 4 -2 Select…

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Q: 7.3 Exercises 1. Use the met hod of undetermined coefficients to determine only the form of t he…

A: We'll answer the first question since the exact one wasn't specified. Please submit a new question…

Q: 12 10 14 11 13 Consider the graph given above. Use the sorted edges algorithm to find a Hamiltonian…

A: Sorted-Edges Algorithm:   1. Sort the edges from lowest cost to highest cost 2. Add edges to your…

Q: 6. Using Second Theorem of Pappus, calculate the volume of solid of revolution when the area of the…

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Q: Let y = Lal: Let L be the line spanned by u. and u %3D Write y as the sum of two orthogonal vectors,…

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Q: Consider the following graph. Let u-(t) = u(t – 7) be the unit step function shifted 7 units to the…

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