Em (n) = n[logn+ (m − 1) log logn + Cm + o(1)] Prove by Induction: Em(n) 1 n n+ 1 Em(n+1) n+1 + m-1 nlogn + an

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A: A number a is called as a quadratic residue mod N if the congruence x^2= a (mod N) has a solution.

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Q: The matrix equation Ax = b means b is the mixture of the columns of A according to the serving sizes…

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Q: Use the Gaussian method of elimination to solve the following systems of linear equations:  [-10…

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Q: Consider the differential equation xy" + (3x − 1)y' – 3y = 0 (x > 0). -3x (a) Verify that y₁(x) = e…

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Q: Find the radius of convergence and interval of convergence of the series, be sure to test the…

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Q: Let A = 1-4-3 4 0 2 4 6 -4 D₁ and b = b₂ b3 Ax=b does have a solution. Show that the equation Ax = b…

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Q: (b) Use variation of parameters to find a particular solution of 4xy" +2y + y = sin (√x); y₁ = cos…

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Q: QB: Solve the following differential equation: d²y dx² +5 dy dx +6y= 3e-2x + e³x

A: QB: Solve the following differential equation: .

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Q: Matrix A is factored in the form PDP-1. Use the Diagonalization Theorem to find the eigenvalues of A…

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Q: Utt(x, t) = -xux(x, t), 0 0 u(x, 0) = 0, ut(x, 0) = x, 0 < x < 1, u(1, t) = sint, t≥0

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Q: (d) (3!x € Z) (3!y € Z) (x³ + y³ = -1) True or False Why? (e) (Vx ≤ R)[x >0⇒ (y ≤ R) (xy > 0)] True…

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Q: 1.16. Do the following modular computations. In each case, fill in the box with an integer between 0…

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Q: 1. Cash Flow. Estimates must present sales projections and sales revenue, operating and…

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Q: 8 (1) F(x) = ft²¯¹e¯¹dt, x³y² + xy + (x² − v² )y=0 0

A: note :As per the instructions we will only solve the part (1) of the question.As per the question,…

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Q: 3 2 N TO 8 9 10 The graph above can be written as y = f(t)ua(t) + g(t)u(t) Where f(t)= a = 3 g(t) =…

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Q: (2) Find the eigenvalue of A and their multiplicities.

A: Since there is mentioned for (2) only.(2)

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Q: Starting with a tone having a frequency of 6080 cycles per second, find the frequencies of the tones…

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Q: Let e₁ 3 -1 and Y₂ = - [ ] ; } » - - }· [1] [B]*-}· and e₂= = 5 6 transformation that maps e₁ into…

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Q: determine the general solution to the system x′= Ax for the given matrix A.

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Q: Define the term permutation matrix.

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Q: Determine a complete solution, y (x): use any applicable method y"-4y=4x-3e¹ y" + y = csex G. H.

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Q: consider the following simultaneous linear differential equations:  (dx/dt) = -11x + 7y, (dy/dt) =…

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Q: 5.2 Simultaneous Equations Ill Write the following sets of simultaneous equations in matrix form,…

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Q: vector field defined by:  F(x,y,z) = xyi + y2j + k What is the expression for the divergence of F? ▽…

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Q: A road C, is defined by the parametric equations as follows:  x(t) = t3,  y(t) = t2, 0 ≤ t ≤ 1,…

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Q: Find ||u|, |v||, and ||u + v||. u = (-2, 1, -1, 0), v= (1, 0, 4, 1) (a) ||u|| (b) |v|| (c) ||u+v||

A: The given vectors  and .We have to find the values of,a) b) c) .

Q: Find the spherical equation for the surface whose rectangular equation is y = xz.

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Q: Determine whether S is a basis for P3.S = {1 − 2t2 + t3, −4 + t2, 2t + t3, 5t}

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Q: 10. Graph at least 2 periods for the function below on the grid provided. Clearly plot at least 9…

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Q: What is the frequency of the tone that is one octave lower than 4480 cycles per second?

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Q: 217 (2² - 2)3(23 – 3)1 dz 5. Calculate integral I 1 La |z=3|

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Q: CHON With c 1 = 0.0001. 3. Consider the function (x-1)^2 + (y-1)^4, which obviously has a minimum at…

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Q: 5. Minimize the function F(A) = (2+2)(2-3)², where is a single variable, by means of Powell's…

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Q: 3. Evaluate, b) (x² − iy² )dz along the parabola y = 2x² from (1, 2) to (2, 8).

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Q: 1 0.5 0.3 3 4 5 6 7 8 । Q2. For the given membership function as shown in the above figure,…

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