(b) Compute the value of the line integral [(2x³yi-xy² j)dr, where C is the path made up from the two line segments from (0, 0) to (1, 1) and from(1, 1) to (2, 1).

Q: Evaluate [F·dr if F(x, y)=(4e³)ī +(4xe³)j and the curve C' is line segments going from (0,0) to…

A: To evaluate ∫C F⇀·dr⇀ if F⇀x, y=4eyi⇀+4xeyj⇀ and the curve C is line segments from 0, 0 to 5, 4 to…

Q: Calculate Vf when f 3x z-y7+ 4x'y+ 2x - 3y-5 at the point (1, 1, 0).

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Q: -2+z) ds over t e point (0, 0, 0)

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Q: F(x, y) = (4x³,3y²) along a path from (0, 0) to (2, 6). Find S F · dř. a) using a parabolic path. b)…

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Q: 4- compute dw dw дх' ду at the point (-2,3) if w = (2x + 3y - 1) ²

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Q: Show that the function u(x,t) = t/2e-*/4 (t > 0) satisfies u, = uxx.

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Q: = Evaluate S₁2₁,22,23] f (2) dz where 21 = −i, z2 = 2 + 5i, zg 5i and f(x + y) = x² + iy

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Q: u = x² + y³ + z*, X = s•t = s2 +t2 y = z = s-t

A: We find complex function

Q: Eliminate the constant: =c₁e²x+c₂e³ 3x

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Q: Find the linear approximation to R(t) = fifth root of t At 1=32. Use the linear approximation to…

A: Introduction: For a continuous and differentiable function fx, its linear approximation is…

Q: A Find the value of J G dL if G = x'a, - xyza, given points P,(1,2,3) and P;(5,0,4) and a path…

A: Given: G=x2ax-xyzaz P1:1,2,3 P2:5,0,4   To find: The value of ∫P1P2G·dL for a path consisting of:…

Q: Show that A Yk= V' Yk+r

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Q: Evaluate e [ f(x, y, z) ds, where f(x, y, z) = 2 + 2y + (z + x) and C is the line segment from (2,…

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Q: What does it mean for the differentiability of a function if only one of the Cauchy-Reimann…

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

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Q: Show that Sa fdx + gdy = Sa - (16x*y²dx + 8yxʻdy) is independent of path: (10,5) –2) (10,5) ,-2) 4…

A: We are given a line integral as follows : ∫1, -210, 5 fdx+gdy=∫1, -210, 5 -(16x3y2dx+8yx4dy)   First…

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Q: Find the linearization of f (x, y)= e²"¬*, at (0, 7 / 2).

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Q: Compute ,f for f(2) +6 + 6i, positively oriented. sin(32) and path 2 that is the boundary of the…

A: Let's see the method of integration. We use residue method to solve this integral.

Q: The direchional derivative of the salan funchion at (l,-1,0) in the direction (i-j+2k) is xy- z- xyz…

A: Given that  Let f(x,y,z)=x^2y-y^2z-xyz To find the directional derivative at point

Q: use implici't differen tiatiom to brind dyldu at the pont (2,2) = 1+y" エ+Scu

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Q: Find the orthogonal trajectories of the family of 2 curves x² + y² = cy A B Ⓒ с D none of the…

A: Given curve x2+y2=cy

Q: Let S(x) be a natural cubic spline that passes thorugh the points (-1,1), (0,2), and (1,1). Then,…

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Q: ) Find an analytic function f(z) = u(xr, y) + iv(r, y) with real part -. -----) u(r, y) = x? – y? +…

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Q: Suppose Vf(x, y) = 3y sin(xy)i + 3x sin(xy)], F = ▼ ƒ(x, y), and C is the segment of the parabola y…

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