1. (x² + 1)² dr

Q: Find a basis of the given subspace by deleting linearly dependent vectors. span of

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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: 3. Find the work of the vector field F(2, y, ) = yi along the curve which is obtained as the…

A: To find the work of the vector field Fx,y,z=yi along the curve obtained by the intersection of…

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

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Q: 2* If ODE of 2nd order and y. 2 x + 3 e-2x, the suggested y, is: C e2x + c2 e3x Yp = Yp = a, x + a2…

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Q: 2ラ(エトリ) = C)

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Q: What is the limit of T(n) as n -> ∞?

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Q: k 0 0 0 1 0 If A = 0 0 1 then det (A) =

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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: O *SimpleTripjava - Notepad File Edit Format View Help Ln 31, Col 1 100% Unix (LF) UTF-8 1 2 3 em 1.…

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Q: Find the local extrema of the following function. .3 f(x,y) = x° - 12xy² + 48y2 Find f, (x.y) and…

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Q: 2 1 -1 Let W = Span 1 1 . Then, the distance and y = 3 -21 11 from y to W is W is

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Q: Evaluate the following sum of iterated double integrals 1 2y c4-2у Ar-z dx dy + 4x-x2 e Az-a dx dy…

A: Due to  change of order we get a single iterated integral and easily it can be evaluated.

Q: If ODE of 2nd order and ye = c1 e²× + c2 e3* ‚Yp = 2 x + 3 e-2x, the suggested y, is:

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Q: a 9. 7 A = a -4 5 9 -9 a nd all values of a that make |A| = 0. Give your answer as a comma-separated…

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Q: The system 4х + 20 y 19 z 1 %3D 5х + 26 y 27 z 4 %3D 4 x + 20 y 20 z 4 = has the solution x = , y =…

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Q: 1 Let A be a 2 × 2 symmetric matrix satisfying A 9. and 2 -2] A 1 [1] with the spectral…

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Q: 2. dz dz dy

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Q: Solve for the laplace transform x(t) = (t+3) sin(t-6)

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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: Let (V, (, )) be an inner product space and let f, g be vectors in V. If || F|| = 4, || g|| = 5 and…

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Q: Question 20 2 0 0] Let A = |0 0 4 1 4 1 Which of the following statements is TRUE about the…

A: Solution

Q: Question 31 2 1 1 U2 = 1 and W =Span{u1; U2, U3}. For 1 Let Uj = Uz = 1 1. 6. in W ? what value oft…

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Q: Find valume bounded by abave Z:4-20 and below by Z-xy 2.

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Q: Let f be on [aib] and differentiable on Caib), Prove that continuous If azo, then there are if X3…

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Q: Find a prime number p for which the equation x? = -1 mod p has no solution.

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Q: Usng polor Codirte to Sad ared bourded by ブニリ ブ=ス

A: Here we use basic polar coordinates to find this.

Q: I. Evaluate the following integrals. 1 · J z(9 – In² r}5/2 1. d.x x(9 – In² x)5/2'

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Q: Question 10 Consider the linear transformation T : P2 → M22 given by [4a + c T(a + bx + ca2) : You…

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

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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: Maximize: z= 2x, + X2 Xy + 4X2 s 12 2x, + 6x2 s 2 Xq + 4Xg s 4 Use the simplex method to solve the…

A: The given linear programming problem is                                          Maximize…

Q: Question 33 You are given that B = {1+æ,1 – x², x + 2x²} is a basis for P2 and [p(a)]g = 3. If p(x)…

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Q: 6. Find a prime number p for which the equation x² = -1 mod p has no solution.

A: Given is a  modular equation.   To Find: A prime number p such that the given equation has no…

Q: Question 31 2 1 1 U2 = 1 and W =Span{u1; U2, U3}. For 1 Let Uj = Uz = 1 1. 6. in W ? what value oft…

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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: Let T : P2 –→ P2 be defined by T(p(x)) = p(3x + 6) and let B = {1, x, x²}. {1, æ, b c a If [T]B = d…

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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: The given vectors form a basis for R3. Apply the Gram-Schmidt Process to obtain an orthogonal basis.…

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Q: Suppose that x is an eigenvector of a matrix A with corresponding eigenvalue 6. Then x is an…

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Q: Let S be the solid inside the sphere p = 6cos@and below the cone Ø = 1/4 Find the volume of the…

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Q: A. LINEAR EQUATIONS WITH CONSTANT COEFFICIENTS d³x 3. dt3 d?x -2 dx - 35 = 0 dt 4. (D³ – 4D² + 4D)y…

A: To find the solution of homogenous linear equation with constant coefficient we assume the trial…

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: Consider the linear transformation T: M22 → P2 given by a (a + 2b + c+ d) + (a + 2b + c + d)x + (a +…

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Q: linear systje is defined by the following equatiosn, -1, -xi + x2 - x3 2x1 + 6x2 – x3 6x1 + 5x2 +…

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Q: Find a prime number p for which the equation x² = -1 mod p has no solution.

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Q: Solve D. E y %3D

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Q: If A = (aij) is the matrix of the quadratic form xi+3x, - x - 6x1x2 + 22x1x3+8x2x3, then the value…

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Q: A doll-manufacturing company wishes to create a display box with a square base and open front side.…

A: Given Let the side of square base of open box is a and height is h. also given surface area is 486…

Q: +00 1 Find the sum of the following convergent series: n? – 3n + 2 n=3

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