Give algebraic proofs of properties (1)u + (-u) = 0 ,(2) (c + d)u = cu+ du

Q: i=| .neN' JSI E (4i +1) = 2n² +3n +1 (2) i=1

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Q: State Leibnitz's theorem. If V1- x² y =sinx, then prove that (1-x) yn+2– (2n+1) xyn+1=n°yn= 0.

A: The Leibnitz theorem is used to generalize the product rule of differentiation. It states that if…

Q: 2. Prove: cot2x - csc²x = -1 %3D

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Q: 1- iz If z = x +iy and w =- z-i show that w = 1= zis purely real

A: Use modulus property

Q: 3.) Prove (cA)" = cCA) %3D

A: Let A be a m×n matrix so A=(aij)  1≤i≤m and 1≤j≤n ie A has m rows and n columns. By AT we mean…

Q: Residue of at z = -3 is (z+3)² Select one: a. -2 b. 2 C. 3 d. -1 е.

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Q: 5. Find the general solutions of the equations i) Zx - 4z,, – 5z, +10z, = cos(x+3y)-sin(x+3y) %3D

A: Since you have asked multiple question, we will solve the first question for you. If you want any…

Q: 2 1-X ie 2=tny then prove that da

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Q: Using Leibniz notation, and given that given thaty = vu and u = 3x³ + 5, apply the chain rule to…

A: Given:            y = u  and u = 3x3+ 5   Chain rule of derivative: If y =f(u) is a differentiable…

Q: a+, 3. f(1)=1** +a cosh /21 +bsinh /21 f(1) =2cos" (21) +e² 4.

A: The Laplace transform of the function f(t) is defined as Lf(t)=∫0∞e-stf(t)dt, since the dimension of…

Q: 16. Use Theorem 12 to show that 2n r=0

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Q: [0 1 If A= find x and y such that (xI +yA) = -1 0

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Q: Find дхду of z = In(x² – y) %3D

A: Derivatives can be defined as rate of change of function with respect to an independent variable. It…

Q: Using Cramer's rule to solve [x + y = 8 lr - y = -2, we obtain and y = 3 2 4 5 1 1. 3 1 1 ||

A: To solve x+y=    8x-y=-2

Q: Prove of disprove if the given DE is exact. 2x^2 +4 =2(3-x^2y)y'

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Q: 5. What is UF, where F = 0? Prove the correctness of your %3D answer / computation.

A: To find- What is ∪F, where F = ∅? Prove the correctness of your answer/computation.

Q: 12. Show that the equation z + iz + 1 = 0 has neither a real root nor a purely imaginary root.

A: Note: According to bartleby we have to answer only first question please upload the question…

Q: Find the the fellowing ODE 's general Solution of ODE'S x³ - X %3D

A: Given ode xy'+4y=x3-xy'+4yx=x2-1

Q: 6. y = C, cos x + C2 sin x + C3 cos 3x + C4 sin 4x ; C1, C2, C3 and C4 are arbitrary constants

A: The given equation is, y=C1 cos x+C2 sin x+ C3cos 3x+C4sin 4x Differentiate this equation up to the…

Q: Ym - 21 , prove that + (n? m² ) yn =o 2 + (2n+1)x Ynts

A: Given y1/m+y-1/m=2x To prove that  x2-1yn+2+2n+1xyn+1+n2-m2yn=0 Solution :  y1/m+y-1/m=2x…

Q: Find all values of the complex function of z for the e^(3z)=1z=x+iy

A: Its given that e3z = 1.  Given, z=x+iyWe need to sovle for z.

Q: 6) limSin (0 – ) 3. 2

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Q: 39. 3x1 - 2x2= -1 4x1 + Sa= 3 Answer: 40. -1 + Sx2=4 -- 3x2=1 41. 6x+ 12-0 Answer: 42, 2x-2r3-4 43.…

A: “Since you have posted a question with multiple parts, we will solve first three parts for you. To…

Q: Example 5.8. Solve du 0 0, ax2 at for (i) u(x, 0+) = f(x), (ii) u(0, t) = 0, t > 0, (iii) u(1,t) =…

A: To solve: ∂2u∂x2=∂u∂t, 0<x<1, t>0 And, the boundary conditions are: ux,0+=fx, u0,t=0,…

Q: 3.Eliminate the arbitrary constant on the given equation: xsiny – x²y- C

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Q: 5. (a) Find the real constants P, Q, R, for which 3 P Qx + R x2 – x + 1° x3 + 1 x + 1 | Show that V3…

A: 5(a)  3 / (x3+1) = P/(x+1) + (Qx+R)/(x2-x+1) ......(1) Now, 3/ (x+1)(x2-x+1) = P/(x+1) +…

Q: 15 Using intermediate value theorem, the equation x² + = 4x has a solution over ]3,4[ 12,31 O 11,21…

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Q: .a TC .bO 2π .cO || 2.

A: I will use the definition of gamma function.

Q: Let z1 = 4 + 4i and z2 = 4 – 5i. Find (in the form x + iy): (5z1 + 4z2)? +i i i

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Q: olve following equation with master theorem T(n) = 2T(n/2) + n2

A: The master theorem says that, If there is a reccurences of the form, If a>1 and b>1 are…

Q: ues of M = 1

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Q: Can there exist two solutions y1, 42: [-10, 10] R to the ODE y = V1+ sin (ry) %3D with yi(-10)…

A: The given differential equation is  y'=1+sin2xy On simplifying this, y'2=1+sin2xy. Hence the…

Q: ху • prove that x +y Example If z = az dz + y.- Əx х. ду

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Q: 5. (a) Solve the cauchy problem given by x²ux + xyuy + xu = Xx-y where (x, y) + (0,0) if u(x, xln x)…

A: Given x2ux+xyuy+xu=x-y where x,y≠0,0 if ux,xlnx=-lnx, x>0

Q: az given that yz*+x2z3 = eyz ax

A: H

Q: 1. (3, x) 2. (3x + 3, y) 3. (y, cos x) 4. (x + y, x – Y)

A: using online vector field graphing we get 1-A 2-C

Q: d 1 - (sec-!r) = dx Prove that xVx - 1

A: Let y=sec-1xsec y =xcos y =1x.....1 Thus sin y=1-cos2y=1-1x2=x2-1x2=x2-1x .......2

Q: Using Euler's equation, show that-: zSinø z{(KØ)} = z2 – 2zCosØ +1

A: The solution is given below

Q: Ho = 0,~Po(x) = { 3 otherwise Hz = 0,~p1(x) = 1 Osxs1 O otherwise

A: It is an important part of statistics . It is widely used.

Q: Find all the joint moments m,1, n and k= 0, 1. . .

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Q: дz дz ду ах of z = x3 + 5x2 y + 6 Find 5. Givenz = " у -4x 6. Find oi, of z = In(xy) 7.Find Әхду "

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Q: 2 2 2 1+ 2 t3十 Cn)和 9 Prove that

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Q: Tofology 2. EX しT X={12/3/4 /5,6 T=Eメ,中っをり,立る, りろ4。 LeT {1,3,4), Topology ? زژه اوم.

A: For the given statement

Q: Example 19-36. If U, = a + bx+cx², prove that 3 U, dx = 2U2 + 12 (Uo- 2U2 + U4) 1 and hence find an…

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Q: True or False 1. If Cov(X, Y) = 0, then X and Y are independent 2. If X and Y are independent, then…

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Q: lestion 25 Consider the following IVP: y" + 3y' + 2y = 12x?; y(0) = a, y'(0) = b

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Q: sin If y = , then justify (1–x² )n. -(2n +1)xy, – n² y,-1 =0 applying Leibnitz's a) theorem.

A: Please check step 2 for the solution.

Q: 8 5 -1 6 (2i-j) x Zij i j

A: Given that z=285-167 The objective is to find, ∑i∑j(2i-j)zij The matrix is 2×3 So, the range for i…

Q: 5. Find the general solutions of the equations i) Z - 4z, - 5z, +10z, = cos(x+3y)-sin(x+3y) %3D ii)…

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Domain

In simple mathematics terms, a domain is defined as the space on which all the possible inputs for the function will lie. It can also be expressed as a set of departures for the required function.