O Given Fley,e)= <6x,- 4z,-4y> Use the parametric descriphion CiP(H = , oŚ€€ to directly evalvate the line integral SE«Tds. ® Find a patential function $s, y, 2)., such that ♡$ = F. © Use the potential fuection found in part B aud thke Fundamental Theo tem of Line Integ rals to evaluate the lme integral ŞETds in part A.

Q: find the angles between the curves v=u2, v=u3, lying on the surface  x=u2+v2 y=u2-v2 z=uv+3u+2v

A: As per the question we are given the parametric form of a surface in 3d as : x = u2 +v2 y = u2 - v2…

Q: Find an equation of the tangent plane to the parametric surface R(u, v) = ((u - sin u) cos v, (1 -…

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Q: Consider the Parametric curve {x=t^3+ 2t^2+t y=t^2−7t+10 (a) It seems to have anxintercept at…

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Q: A particle travels in the xy -plane with a path defined by the parametric equations x(t) = t - 3 and…

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Q: At point (6, 3, 162), find the parametric equations for the normal line to the surface z = 5x^2 -…

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Q: 6) x² + (y – 4)² = 4 Center Radius

A: The given equation is x2+(y-4)2=4This is in the form of (x-h)2+(y-k)2=r2 which is a circle equation…

Q: За and the equation of the tangent line to the curve at the point (a,b) is y = 2 - If f(x) = -x- x +…

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Q: ind the parametrization of the curve defined by the intersection of the two surfaces y = x^2 − 3z^2…

A: To find the parametrization of the curve defined by the intersection of the two surfaces  and ,…

Q: Where an Interior point Exists?

A: Interior point: Let S⊆ℝn.  A point a∈ℝn is said to be an Interior Point of S if there exists an…

Q: How can I parametrize this 3D shape with two variables? x ≥ 0, 0 ≤ y ≤ x, x^2 + y^2 ≤ z ≤…

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Q: Compute dr where C is the ellipse 4x² + 2 = 4 (with counterclockwise 32 motion) and F(x, y) = (2++²…

A: Given Information:The vector field is given as .Ellipse equation:  with the counterclockwise…

Q: Find the directional derivative of f(x, y) = In(e"- 3y) at the point (0,0) in the direction of 3i +…

A: We are asked to find directional derivatives of function.

Q: к Determine aT, aN and K for the space curve r = (2e^t)i + (t)j + (e^2t)k.

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Q: Determine the total distance covered from t = 1 to t = 3 from the given parametric equations: x =…

A: Let's find the total distance covered. = d

Q: Find an arc-length parametrization of the line passing through (1, 0, 1) and (1, 2, 3). Upload an…

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Q: Denote that G is a parametric curve x(z) = z2-z-2 y(z) = z²-=2+z Calculate whether if G is concaving…

A: Given parametric curve G: xz=z2-z-2yz=z3-12z2+z We have to calculate whether if G is concave up or…

Q: Q3b): Compute zdz over several contours (i) The line from 1 to 1+ i. (ii) The circle of radius 1…

A: let fz=1z.  Since f(z) has an antiderivative in an open region D, then the line integral over given…

Q: What is a parametrization of a curve in the xy-plane?

A: we have to tell what is parametrization of a curve in the xy-plane?

Q: (x+ 4)² + (y – 4)² = 4 Center Radius

A: Compare given equation with (x-h)2 + (y-k)2 = r2

Q: Solve: b,c and d part  (b) Give parametric equations for the tangent line to the curve C at the…

A: Given curve is r→(t)=t, t, t2 we can write the above r→(t)=ti+tj+t2k Here x(t)=t, y(t)=t, z(t)=t2…

Q: Give a parametric representation for the cylinder x^2+z^2=121

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Q: Evaluate S (* + 7)i + (2») 5).dF. where Lis the quarter-circle with parametric form z = cos (t) and…

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Q: -ind the oarame

A: The equation of the parametric curve is: x=2cosπt-1y=2-3t2+4t3 We have to find the equation of the…

Q: Cannot solve

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Q: Find an equation in spherical coordinates whose graph is the parapoloid Z=(X^2)+(Y^2)

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Q: Find parametric equations for the path of a particle that moves along the curve y=x^2 from (1,1) to…

A: The given points are (1,1), (-1,1) and (1,1) and the curve is y=x^2. The particle moves along this…

Q: Solve the differenttal equat on 1y +dy_64=12x-50 Sin 2x dx? doe

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Q: Consider the curve parametrized by x = t +1 and y = t6 + 4t. dy in terms of t. d.x a) Find Preview…

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Q: Write an equation of the tangent plane to the parametric surface: r(u, v) = (u + v)i + 3u^2j + (u −…

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