Use Green's Theorem to evaluate >[2²y² dz + (yz²³ + y²) dy where Cis shown below. 90 O-384 O-48 (4,2) N (4.-8)

Q: Show that 5+6Z is a unit in Z/6Z.

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Q: Evaluate L{t cos 4t} s2 +4 b) 52 – 4 s2 + 16 c) s2- 16 s2 - 16 d) s2-4 a) s2 +4 s2 +16 O a O b

A: None of the options are correct

Q: TEST FOR HOMOGENEITY: 2. x² - 5xy - 4y²

A: The given function is x2-5xy-4y2 We need to test the Homogeneity.

Q: Evaluate I 5/2 U (4-u) du · Su² 3/2

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Q: موضوع الدرس: Find the sewera (BY COS X + 4X +2x S * 6 ution of Jdx + (3 $ inx+3) dy ap

A: The given differential equation is         (3ycos x + 4xex + 2x2ex)dx + (3sin x + 3)dy = 0 We can…

Q: 18 16х + 17 dx Evaluate

A: ∫xndx=xn+1n+1+C where n≠-1

Q: Evaluate: L(e* -3t * sinh 7t).

A: Given: Le-3tsinh7t

Q: Q.1A) Evaluate 2 (4-x*) 4 cosy dydx 4-y

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Q: 5. Use geometry to evaluate (V4- x² dx 2 O 2n O 4t

A: Solution:

Q: -4 6. |a + 3|dx – 1)³ydy -1

A:

Q: Prove that B(m, n) = B(m + 1, n) + B(m,n + 1)

A: given,

Q: In(1+ 5.x?) 2 – 3x Differentiate with respect to x.

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Q: Evaluate ze -dz, where C is z+ 2 ((+2+2)?

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Q: 7. Evaluate * (D5 - 3D4 + 8D³ + 16D² - 9D - 13)y = 0 y = (C₁ + C₂x)e¯x + С3ex +C4e²x cos3x + C5e²x…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Is Q closed over multiplication? (Y/N)

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Q: y (0, 2) (-5,0) a. - 5x + 2y = 10 b. 5x-2y 10 C. -2x+ 5y= 10 d. 2x-5y = 10 %3D

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Q: re 1 da Ji rVI- (In x)²

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Q: (x-1)2 (y+2)? What are the endpoints of the conjugate axis of 25 - 36 O (1 ± 5, –2) O (1, -2 ± 6) O…

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Q: Does the limit t limit x"- 4y exist ? (2,Y) -) (0,0) Explain your answer

A: We need to check whether the limit limx,y→0,0x4-4y2x2+2y2 exist?

Q: The residues of f(z) O-4/9,-4/9 O-4/9, 4/9 O 4/7,4/7 O 4/9,-4/9 O 4/9.4/9 4z (z − 1)(z + 2)²

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Q: 12. Evaluate the expression using de Moivre's Theorem. Write your answer in standard form z = x +…

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Q: Which one of the following is isomorphic to Z4 x Z6/((2,4))?

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Q: 21 12x + x4 Evaluate 19 dx - 6x2 + 7 x3 – 19x + C, Where C is the parameter 6x² + 7 x³ 19x + C,…

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Q: n (3+ form atbi -64)(12- J-4

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Q: Find the distance between 4y + 3x = 4 and point (0, 5) O 3.2 3 O 3.4 O 2.8

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Q: 1. Multiply. x' x x a. 5x'z x- 2xz2 - 4xy x-3x'yz g. 2a'b'c x 2abcd C. e. of

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

Q: 27x dx= |4-9x² 3x -1 3 xV4-9x² +C 2 a) 4 sin 2 3x b) sin 2 1 4-x² +C 2 3x с) 2sin -1 2 3 xV4-9x? +C…

A: The solution as follows :-

Q: 1- Let z,=-5+11i and z3=2-21. Find in the form x+iy a) Re(1/2,) b) 1/ Re (z,) c) z,-z,? d) (z1/z2)

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Q: E Show that x'+ 3x+ 2 has 4 zerosin Ze

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Q: If z = 1+ eie Find z*, z?.

A: Conjugate of a complex numberz is formed of same real part and opposite imaginary part. Its…