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A: Given:
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A: It is given that,
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Q: Sketch the plane curve. r(t) = 2ti-tj, [0, 2] y -1 y 2 1 Find its length over the given interval. 2…
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Q: H.w.L Findthe angie between the Plane X+y+z=t -and tle X-yplane- (2=0).
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![Sketch the plane curve.
r(t) = 2ti – tj, [0, 2]
y
y
2
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-1
1
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-1
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-1
-1
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y
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-1
Find its length over the given interval.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F66c26782-6b16-42b4-972e-8e19be418db2%2F45533b45-d448-481f-acfa-c5d5054d9657%2F1hq5g6p_processed.png&w=3840&q=75)
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- Sketch the plane curve r(t) = ti + t2j and find its length over the given interval [0, 4] .Find the points on the curve x2 + xy + y2 = 1 in the xy-plane that are nearest to and farthest from the origin.Consider the curve C parametrized byx = (t^2+1)/(t^2-1) and y = (2t)/(t^2-1) for all t in (−∞, −1 ) ∪ (−1, 1) ∪ (1, ∞) .By squaring both x and y, find an equation of C in terms of just x and y (no t):
- Find the DE of tge familiy of plane curves described and sketch some of its members 1. tanx-2x3y=cfind the work done by F in moving a particle once counterclockwise around the given curve. F = (4x - 2y)i + (2x - 4y)j C: The circle (x - 2)2 + ( y - 2)2 = 4an equation for the plane tangent to the graph of z=9-6x^7+3y^3 at the point where x=1 and y=2 is:
- Sketch the space curve r(t) = ⟨2 sin t, 5t, 2 cos t⟩ and find its length over the given interval [0, π] .Find the length of parametrized curve given by x(t)=12t^2−12t, y(t)=−4t^3+6t^2+9t where t goes from 0 to 1.Sketch the plane curve r(t) = a cos3 ti + a sin3 tj and find its length over the given interval [0, 2π] .