1. The integral of J, \z|dz along any closed path y is 0.

Q: -1-y 3) Evaluate the integral dxdzdy?

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Q: Evaluate the integral S dy -4y+8 dy 1,200 y 4y + 8

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Q: B)Is w = Ze² analytical function or not?

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Q: Show that the function y = x1/2, x > 0, is strictly concave

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Q: Show that the line integral | 2.xe- dx + (2y – a²e¬") dy is independent of path and evaluate the…

A: Here we have to show that the given line integral is path independent and evaluate the line integral…

Q: What should be A for the path independent of (2,4) 2Ay – x dy. y? XY + A (1,2) over evaluate the…

A: Consider the provide integral,

Q: Evaluate fv*+1dx x2 A. 를 (1 +즐)를 -를 (1+ 즐)를 :. 를 (1-즐)를 -를 (1-2)를 + C + C + C D. + C Evaluate the…

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Q: . Evaluate the line integral where F x² + y² = 4 in Q1, Q2, and Q3. - (1, 2y) and the pathway C is…

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Q: prove that ਰ Apply the calculus of residues to dx (1 + x²)² - π 4 .

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Q: 2. Rewrite the integral f(x, y, z)dzdxdy using the order dxdydz.

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Q: Prove that f (z) =zz is nowhere analytic

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Q: if r'y-- 2y + 1.

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Q: Ex.2. Prove that the complete integral of the equation (xp + yq - 2)² = 1 +p² +q² is (ax + by + cz)…

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Q: Evaluate the line integral of F = [-2.2³ – 2 ·x, −2 · z² + y² — 2, y³ + x] along the z-axis from z =…

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Q: 13. Verify if div(curl F) = 0 for F = (x - y) i+ (x + y)j+ zk. %3D

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Q: Prove that 3x +8 Viv = dr dy: %3D where R [-1,1] x [0, 2).

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Q: Show for all x, y in R |x+ys]xl + ]y!

A: consider left hand side  and use the result x=x2 x+y=x+y2=x2+y2+2xy≤x2+y2+2xy≤x+y2=x+y

Q: Verify Green's Theorem by evaluating both integrals y? dx + - x² dy = da ду %3D ax for the given…

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