Determine whether the equation is exact. If it is, then solve it. (2x + y)dx + (x - 2y)dy = 0

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A: Given: We have to solve for  correct upto  decimal places.

Q: Determine to the 24 +22+8=0 Need (f(2)| > | g (2) on 121= 2 19 (2)| = 22 +8 ≤ 2/2/+8 = 2·2+8 12…

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Q: 43. Use Green's Theorem to evaluate the line integral along the positively oriented closed curve C.…

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Q: the section D of this question wasnt solved

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Q: S 4. Find the Taylor series of cos x and show that it converges to cos x for xER. 5. Repeat the Q4…

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Q: Find the area inside the graph of r = 5 - 3 sin (0) and outside the graph of r = 5 - 3 cos(0).

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Q: Evaluate the Cauchy principal value of the given improper integral. 100x² sin(x) x² + 6x + 10 dx

A: Let                 where I.P. means Imaginary part             Let                 for…

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Q: Let √5 0 2 √5 Find a full size form SVD (singular value decomposition) A = 0 /15 of A.

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Q: 3. Write as a single logarithm and explain your steps and logarithmic laws used. 1 2loga + log(3b) —…

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Q: You deposit $2000 into a savings account with an APR of 5.5%. (a) Compute the amount of interest you…

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Q: dy Let y = f (a) be the solution to the differential equation d = 3x + 2y with the initial condition…

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Q: Find the mass of a wire that lies along the curve r(t)= (t² – 8) j+2tk, 0≤t≤2, if the 3 density is…

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Q: 14. Q = /5 16. Q = 2= [₁ 1-2 21 32 -2 3

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Q: 1. 2. The function f(x) = (+)* a) (-1,4) passes through the point b) (1,-4) Х The function f(x) = ()…

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Q: Are there any situations in which function composition will be commutative? That is, are there any…

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Q: Let u (x,y) = e ² cosy + x² - y² 2 u is harmonic Find all v (xay) such that u(xsy)tiv (xsy) is…

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Q: In Exercises 27-30, calculate ||x||. 1+i 2 27. x = 28. x = 3+i 2-i

A: Norm:

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Q: Show that det [1 1 0 0 1 1 0 0 001 0 0 0 1... 0 0 ⠀⠀⠀ 0000 1000 0 0 ... 1 1 01 = 1+ (-1)"+1.

A: The given matrix is a circulant matrix with a special structure. A circulant matrix is a matrix in…

Q: Let A = 11 -1 -7 -1 5 -1 -7 -1 5 (a) Show that x¹ Ax ≥ 0 for any x € R³. T (b) Find a non-zero…

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Q: Use 2.2.24 to solve 2.2.25 My argument should work for any alpha and any z_*

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Q: Boundary-Initial Value problem

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Q: The matrix 8 4 -4 0 -4 -4 0 has two real eigenvalues, one of multiplicity 1 and one of multiplicity…

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Q: Let S denote the surface of the box [-2,3] x [-4,2] × [0,3], ori- ented outward, minus the disc that…

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Q: 4. For an odd prime p, suppose that (=) = 1 and consider the congruence x² = a mod p. (i) For p = 3…

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Q: eigenvalues

A: This is in the form

Q: 35. Find the area of the part of the plane 4x-2y-z4 that hesabuvo the root)c [-1, 4]X[3, 7]. a. 51…

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Q: sin(x) = x mx 110 (lerror] < 0.01)

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Q: 3. Solve the system pdf notes and videos. dx dt dy dt = = 4x - 3y 2x-y using the eigenvalue method…

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Q: 4 7 670 |--[31] - -3 -6, b 2 3 Select true or false for each statement. Let A and c = 0 []·.· 1. The…

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Q: 5. Decide whether R Q is countable or uncountable, and prove your answer. You can use what you know…

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Q: Let ² = (62 +6x4) ² + (2y +62 + 6sin (y+)) j +(6x+by+ 2e²") E. (a) Find curl 7. (b) What does your…

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Q: 8. Answer the following questions about the functions whose derivatives are given below. What are…

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Q: curl of Vf. Find the gradient Vf of f(x, y, z) = x²y+3xyz-2y²x and then find the divergence and

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Q: D. What is the average rate at which the rocks at Point A have moved away from the spreading axis…

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Q: 1. The periodic function f(x) has period 27. It is defined in the interval 0≤x≤ by f(x) = 2x² (a)…

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Q: 3. Use a double integral to find the area of the region bounded by the curve r = 6-5 cos 0. -10

A: We are given the cardiod then need to find the area of the given cardiod.