Evaluate the commutators [Lz, r²] and [Lz, p²] (where, of course, r² x² + y² +z? and p? = p? + p; + p?).

Q: Show that R2 =

A: Then, V =Span(S), if every vector in V can be written as a linear combination of elements of S.

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Q: В. Let a %3 -в -2 1, Find a value for k so that the dot product of a with = Lk 1 4]is zero.

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Q: Q: Show that the functi on f:R →R given by f (x) = ax +b, where ab e R, a #0 is a bijection.

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Q: I Cimpute-he the following bylk matnin detexminant 4 3 3 6 4 2

A: Let A be the given matrix - A = 1111123413610141020A =…

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Q: Prove that r - 2 does not split in Q ( V2e*).

A: given   x3-2    and    Q23e2π3i now…

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A: SOLUTION-

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A: According to guidelines we solve one question.

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A: Derivative of function

Q: Prove that Σ", (2i-1)-. .

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

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Q: Find all positive integers x, y, z satisfying x · y · z² = 5xyz. '*

A: Introduction :Given , positive integers x,y,zwe have asked to find the values of x,y,z which…

Q: tan X Select the rules - Alyebra -Recierocal -Quotien4 Py tuagoren ) Oda lE ver -Evaluation 58idate…

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Q: Describe the long run behavíor of f(r) = r° – 3r° – 2rª + 5 %3D - -

A: The long-run behaviour of a function is the behaviour of the function at its endpoints of the…

Q: the smallest possibl product of the two numbers x>= 0 and y<= 0, such that 2x-y=120 is:

A: Let x and y be two numbers such that  x≥0,y≤0, 2x-y=120y=2x-120

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Q: 3) By changing the independent variables x and y to u and v by means of the relations u xay, v = x +…

A: Apply chain rule

Q: What is tle sum of P(x) and Q(x) if P(x) = 4x² + 6x – 9 and Q(x) = -7x² - 12x + 8? %3D 1. -3x2 - 18x

A: GIVENP(x) =4x2 +6x-9Q(x)= -7x2-12x+8

Q: √x³√1-x² 2

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Q: 82z 82z + 8x2 82z If z = x + y lnxy, show that x- = y², y2. 8y2 ID 8x8y

A: Given, z=x+ylnxy We need to show that,    xδ2zδx2+δ2zδxδy=y2δ2zδy2

Q: Show that Rsta is Hausdorff.

A: Note that a topological space X,I is said to be Hausdorff if (and only if) for every distinct points…

Q: Express (2ay + 2x – 1) – i (a2 – y? – 2y) as polynomial in the binomial argument z = x + iy. iz + 2z…

A: Solution

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A: To show that a value or number satisfies an equation, we substitute the value in the equation and…

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Q: prove that two vectur ae orthognal A = x + 4y+32 B =4x+2y-42

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Q: Describe the behavior of the expresion as x → 4† and as x → 4¯. Enter oo for ∞ and -oo for – o. 4x…

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Q: Express (2ry+ 2x- 1)-i (x2 - y-2y) as polynomial in the binomial argument z = x+ iy. O iz? + 2z + 1…

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Q: Consider R2 with the weighted inner product = 2ujv1 + 4u2v2. Then ||(2, 3)|| = a) V13 b) V44 c) V20…

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Q: Use substitution method to prove step-by-step that (P^Q)^(P = ¬(Q^R))^(S = R) = –¬S.

A: We are asked to prove the following using the substitution method, P∧Q∧P⇒~Q∧R∧S⇒R⇒~S We will show…

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A: Given equations as yi=cijxj and bijcik=δki

Q: HwO Use Gramer Rale to Find 4,2 -2x + 3-Z = 1 X + 2y-2- 4 -2x -y +2 = -3

A: As per guideline we have to solve only one

Q: (P^Q)^(P = ¬(Q^R))^(S = R) = -S

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Q: 5lim V3+x-J3 8→0

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Q: Express (i)(T) J3(x) in terms of J₁(x) and Jo(x) (ii) J₂(x) in terms of J₁(x) and Jo(x) (iii) J4…

A: Note: since you have posted multiple questions. As per our guidelines we are supposed to solve only…

Q: Use substitution method to prove step-by-step that (PAQ)^(P = –(Q^R))^(S = R) = ¬S.

A: We are asked to prove the following using the substitution method, P∧Q∧P⇒~Q∧R∧S⇒R⇒~S We will show…

Q: Verify that * / II 21 ?х ду 224 ду ох - for f(x, y) = 4x4y3 - 6xy5.

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Q: 5. Compute divF and curlF for F = x²yî – (2³ – 3x)ĵ + 4y²k.

A: In this question we have to find the curl and divergence of the given vector which we can find out…

Q: Express (2.ry+ 2x - 1) – i (x2 – y? – 2y) as polynomial in the binomial argument z = r+ iy. O -iz? +…

A: Solution

Q: Use square WXY Z: 1. If WY 9r - 2, ZX = 5r + 14, then z = 2. If mZZWY = 8x - 3, then z 3. If mZZSY =…

A: According to guidelines we should have been able to solve only three sub part of the question

Q: Prove using soundness (Required): (∀x)A → (∀x)B ⊬ (∀x)(A → B).

A: The proof is shown below.

Q: Use generating functions to determine the number of integer solutions for x + y + 2z = 29, x2-2, y >…

A: Given that x+y+2z=29 As for each x,y,z are non negative. The variable for x is, The variable for y…

Q: For f(x) = 4x + 12x, find the number c in (-4, 1) guaranteed by Rolle's Theorem. %3D (Use symbolic…

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