338. [T] Use a CAS and Stokes' theorem to approximate line integral /[(1 + ykdx + (1+ z)xdy + (1 + x)ydz, where C is a triangle with vertices (1, 0, 0), (0, 1, 0), and (0, 0, 1) oriented counterclockwise.

Q: Consider the following statements about the surface of the equation z = 2x / (ln (y) +1) - (y + 1) /…

A: The given function is z=2xlny+1-y+1x and the given point is P-2,1. The directional derivative of a…

Q: = (1 – t)i + (4 + t)j ess your answer as an ir erical answer only.

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Q: Find a number a so that the change of coordinates s = x + ay, t = y transforms the integral ff dady…

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Q: Find the tangent plane to the surface of at (1, -2) and a normal vector. f(x, y) = ln(x² + y²)

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Q: Q.1) Use the polar integral to evaluate /1-(r-1)² r+y dydr 1² + y?

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Q: (5) Use Stokes' Theorem to find the line integral |(* + 2y°)i + (y + z°) +(= + 2r*)k) • dř where C…

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Q: Q. Let f(z)= u(xy)+ i V(x>Y) be analytic function and Z= re Find the Cauchy - Reimann eguations in…

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Q: 2e? Let f (z) = -Let C'be the circle z = 7in the counter-clockwise direction. (z – 3) (z – 5) Part…

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Q: Differential Equation: Solve the given LDE: y^(6) - 64y = 0

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Q: 2. The vector function Ř(u, v) = (sin u cos v, sin u sin v, cos u), (u, v) E [0, 7] × [0, 2m] gives…

A: Here, the parametric vector function for the surface is given by R→u,v=sin u cos v, sin u sin v, cos…

Q: (u, v) ~ (x, y) as (x, y) → (0,0) that will bring to the sum of squares z = A1u? + A2v² the…

A: given u=ux,yv=vx,y   and u,v~x,y as x,y→0,0 define a function z=λ1u2+λ2v2 where…

Q: Find the exact value of | (yi+ vxj) · dr where C is the parabola y = x² from the origin to the point…

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Q: Verify the line integral and surface integral by relating them to the Stokes' Theorem where C is the…

A: Stokes theorem    ∫CF→.dr→=∫∫ScurlF→.dS→ Where S  be a smooth surface  bounded by a closed, smooth…

Q: Evaluate the line integral f F dr, where F(x, y, z)= -sin xi - 3 cos yj+xzk and C is given by the…

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Q: 10. Use Stokes' Theorem to evaluate ||(V×F)· dS where F= (z,2x, y) and Sis the hemisphere of x' + y?…

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Q: Let C be the closed, piecewise smooth curve formed by traveling in a straight line between the…

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Q: Find the work done by the force F- Tyi + (y - ±)j over the straight line from (0,0) to (3,6).

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Q: 7. For the vector-valued function √t-1 ln(2t - 1) t² - 1 r(t) = (VI- t-1 2 COS πt rt), (t (t = 1):…

A: Let us solve above problem

Q: Calculate the flow in the field F along the path C. F = (x - y) i - (x 2 + y 2) j; C is curve from…

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Q: Use Stokes' Theorem to evaluate ſc F. dr. C is oriented counterclockwise as viewed from above. F(x,…

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Q: the value of $[(3x + 4y) dx + (2x + 3y2) dy] around the circle x² + y² = 4. Find the line integral…

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Q: Verify the Green's theorem for the following integral O sinydx + (x – cosy)dy where curve C is the…

A: Answer