Use Green's Theorem to evaluate(¹-28) O-96 O-75 O 105 -2y) de- (62-4ry") dy where C' is shown below

Q: Let {(=) = In ="(z +2)*(z² + 9)] f'(x) =

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Q: (7) In general, (SOT)CSnT.But, (SnT) + SnŤ.

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Q: )(2n) for conplex number sequance show that if lm En=1 then 3no fN such that for for Hn 7 no o Znto.…

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Q: (3Vr + 2e) dx.

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Q: Find Cn in terms of C0 when: 1. Cn = Cn-1/(3n2 + 4n): (Note that C1 = C0/7, C2 = C0/140, C3 =…

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Q: Explain why it is not necessary to use the Quotient Rule to compute

A: Because in the first expression x is in the numerator and we are doing partial derivative with…

Q: c2π cos² t 13+ 12 cost dt

A: The Cauchy Residue theorem is a part of the complex analysis. By using the Cauchy Residue theorem we…

Q: Q₂i- If show that utt ч (хо) ut (x,0) - a 9/x). Z 3 u (X, Z) 2 Ux(xt) = a as 1x1_-2 ux 9. 2 u XX…

A: Using D'Alembert solution for one dimensional wave equation.

Q: In(x-1) 33 Differentiate with respect to x. 2x + 3

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Q: 0.2 Differentiate In x+1, with respect to x. x²-x+1

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Q: Evaluate the Cauchy principal value of 2 x 50% -dx 8 x 2 (x² + 1)²

A: We have to find Cauchy Principal Value of the given integral.

Q: 1. Show that cosh 4x = 8cosh“x - 8cosh? x + 1 .

A: Given problem:- Show that cosh(4x) = 8cosh4x - 8cosh2x + 1

Q: 4. If x = cose + isin0 & 1 + V1– a² = na then prove that 1+ acose =(1+ nx)(1+) %3D 2n

A: Given, x= cos θ+i sinθ and na=1+1-a2      To prove:  1+a cosθ=a2n(1+nx)(1+nx)       Let  x=…

Q: x² – 4 Evaluate: A =Vx2-4+ sec-스)+C ⑥ -Vx2-4+2 sec-스)+C =V x2 – 4 – 2 sec + C (D =2Vx2-4+ sec-1스)+C…

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Q: dx Sx²+ 4 2. 多.区

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Q: 2 Find (5a" + 4a*) da 1

A: We can find the integration value as below

Q: If B' is of order 2x3 and BA is order 3x4, then A is of the order T

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Q: dx_ -In x – 2 |x+2 X - + C x² – 4 - 4 Select one: O True O False

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Q: 9. Prove the following algebraic identity: (a - b)(a? + ab +b?)=a' -b'

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Q: (15 – b) (9 – b) - z = 6. 6. För a = 1 och b + 3 saknar systemet lösningar. För a = 1 eller (4t) , y…

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Q: Show thet the Se nng + ベ+」 (+リ(2ペ+)+ ()) (ox) ナ (A+)(2p+1) (P+1) (28+1)(38+) (uhse a>0, B70) (uhse…

A: A series is said  to converge  if  the sequence of partial sums  converge. There are various tests…

Q: Simplify: 8x+7 y-10 9xy 11axy 79xy+77y+90x O A. 99xy 79xy+77y+90x 99x²y 90xy+77y+79x 99x y .2 O B.…

A: 8x+79x2y-y-1011xy2=(8x+7)11xy2-(y-10)9x2y9x2y(11xy2)

Q: de a+bcose' where a> bl. Hence or otherwise evaluate 2n de √√2-cose 3

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Q: Zero(s) of multiplicity one: Zero (s) of muit iplicity jwo Żerols) of muitnpncitj inree:

A: multiciplicity is no of times repetation of zeros that is known by putting given equation to zero.

Q: Evaluate L{3(sin² 2t )} 24 24 24s 24 а) s(s² + 4) b) d) s(s² + 16) s(s² + 16) s(s² – 16) a O Option…

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Q: prove that theta(2m) = theta(m) when m is odd and theta(2m) = 2 theta(m) when m is even

A: We can start by using the definition of theta notation to prove these statements. Recall that theta…

Q: Evaluate L{cos² 3t} s² – 18 a) s(s² + 36) s2 – 18 b) s(s² – 36) s² + 18 c) s(s² + 36) s2 + 18 d)…

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Q: 2 Evaluate: ²₁²(x²-y²² du dt

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Q: 1. (а) 52x $* (b) 3' x 32 - 5 2. (a) k* x k? (b) m³ x m 3. (а) у к (-у") (b) -x (-)

A: Given: 1.(a)52×56  (b)33×332.(a)k4×k7   (b)m5×m9   3.(a)y2×(-y10)  (b)(-z3)×(-z4)

Q: Prove the follawing identities. 4-V. 4- V = AV (a) (b) M8 = A/1+ 4) (1+ A)" 2. (C) 4/f = I for Afn-…

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Q: DeMorgan's theorem states that Select one: a. (A + B)' = A' * B b. (AB)' = A' + B' c. A' + B' = A'B'…

A: We are given some statements to verify De Morgan's theorem. We can do this in the following way:

Q: 5. Evaluate | (x² +1)* dx using trigonometric substitution as your first step (not a u-sub as your…

A: The solution is given below in the next step: