Prove that Σ", (2i-1)-. .

Q: x+y uis = 1 n upi = no • prove that x-+ y-

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Q: 5. (6 + 15i ) 3

A: this is a problem of complex analysis.

Q: Suppose the conjugate z is equal to the reciprocal 1/ z. What are all possible z's?

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Q: The convolution of e2t ® sin(3t) S is | e2Usin(3t – 3u)du e2usin(3t – 3u)du Se-2usin(30)du…

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Q: Prove that the following relationship is true: nCr + nCr + 1 = n + 1Cr + 1

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Q: If I, = [x^tan"x dx, Prove that (n+1), + (n-1),,2 ° п 1 %3D 2 n

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Q: Prove using the IVT. For all positive integers k, cos x = xk has a solution.

A: Intermediate value theorem: Let f be a function continuous on a closed interval a,b. Let k be number…

Q: 25 If A E M, is symmetric, prove that AT is symmetric.

A: Symmetric matrix

Q: alue of the pur C: |z| = (:-1)(z-

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Q: How did they calculate what T does to the elements of B?

A: You want to know "How did they calculate what T does to the elements of B?" We have  B=1, x, x2, x3…

Q: Q6:-Prove that: y" = 1 if y=;csc (tan"

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Q: prove using the IVT. √c +√c + 2 = 3 has a solution.

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Q: Prove this! P (an) = W/ NM) [M-N (p-q)" ] 8 Npq %3D exp

A: your question is not clear i think some error in the question plz confirm it.....

Q: 2. Let X, Y c R. Prove that X U (Y – X) = Y if it is true. If not, give counterexamples to explain.

A: Given statement is false.

Q: S Prove that L(cos 3t) : %3D (s2+9)

A: We know that Lf(t) = ∫0∞e-stf(t) dt Then Lcos 3t = ∫0∞e-st cos 3t dt                             (1)…

Q: Prove that i 224 s 2xP for xzO, y zo i and 1 t L-l with p>

A: Given that x,y≥0. And 1p+1q=1 with p>1. Consider gx=xpp+1q-x. Then g'x=xp-1-1 and g'x<0 when…

Q: S Prove that L(cos 3t) (s²+9)

A: Given L(cos3t)

Q: 2. (– 13 + 3i)31

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Q: Let x, y E Z. Prove that if 3 ł x and 3 ł y, then 3|(2² – v²).

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Q: HW klx) = 2x+5 ㄱ 1. Find ke-¹(x) 2. Prove by kokorklok

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Q: 1 Assume that 1 < a < b_and equation is solvable. + x = Show that this * – b'

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Q: 2.Prove that I (sinwt) : s2+w?

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Q: Sketch the set of points satisfying: |z - 1 + 2i| = |z + 3 + i|

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Q: Q4 Prove that E(",") = ("::)- () .n 2mzr. %3D +1 +1

A: we have to prove that                                                   ∑k=0mn-kr=n+1r+1-n-mr+1 now,…

Q: 57. Use the substitution u = x/3 to prove dx 1942=tan 1+0 www C 9+x² 3 3

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Q: Prove that for all values of the constant A, eAInt = e In.

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Q: Prove that eie ei(0+2K) ,where k = 0,±1, +2,...., = D

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Q: nd C such that AC=E

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Q: W Given: OWXYZ with diagonals WY and XZ Prove: 21 = 22 2

A: Given: In figure  WXYZ is a rectangle with diagonals WY and XZ. To show: ∠1≅∠2

Q: (b) f(z) = tan¯"(5z) - (In(2"))®

A: We have to find derivative

Q: (-1+i/3)°, by using deMoivre 's theorem

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Q: 6. so be it r = 3xi + yi – 2zk and f (r) : -- where |r| = r find all of grad(f) and div (-)

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Q: ) Prove that sac"()/T sec

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Q: of af 42. Assume that w = (х, у) — ху, and (х, у) ду dw dw Find and at ds

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Q: Verify that the conclusion of Clairaut's theorem is valid, that is, that uxy = uyx u = x4y3 - y3…

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Q: Consider (Ru) .f : R->R -3 X3o 3. X70 Prove Pex) is Con tinuos onR-301

A: Given that                                      f:R→Rf(x)=-3; x≤03    ; x&gt;0 we have to prove that…

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

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Q: B. Prove by direct proof general. P: Vn e ZE, (n – 1) (n+ 1) e Z,

A: I have solved B; you just need to expand (n-1)(n+1) and then use the fact that square is always…

Q: Q1. Prove that KT = = -.

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Q: Prove that S, pm (x)Pn(x)dx = 0 if m# n ? %3D

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Q: . Prove that, e²i = e²1=22. ez2

A: Let,z1=x1+iy1z2=x2+iy2z1-z2=x1+iy1-x2+iy2=x1+iy1-x2-iy2z1-z2=x1-x2+iy1-y2…

Q: 4. Prove the statement of 3 on page 9 of lecture notes 10, i.e., SSE xa-1)(0–1)*

A: The given model is, yij=µ+Ai+Bj+∈ij    where, i= 1, 2.......a and  j= 1, 2.....b∈ij~N(0, σ2∈)Testing…

Q: Ihow do you bnd the imit of as x approaches 0?

A: The limit of x+1-1x as x approaches to 0

Equations and Inequations

Equations and inequalities describe the relationship between two mathematical expressions.

Linear Functions

A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.