- 4. Let w = 3y da + 3x dy + dz be a one-form on R°. Find a parametric curve a : [0, 1] → R° such that | w = Enter the three component functions of your parametric curve, as functions of a parameter t. a(t) = (|

Q: Let R(t) = (t²,1 − t², t) and r(t) = cost. Determine the parametric equations of the line tangent to…

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Q: For the smooth curve r(t), find the parametric equations for the line that is tangent to r at the…

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Q: 4. If y = tx, where t is the parameter, what are the parametric equations of the curve x' +y° = 4xy?…

A: The solution is given as

Q: Find a parametric form of the closed curve x? + 2y2 + 2x – 4y – 13 = 0 in the xy-plane with a…

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Q: Suppose parametric equations for the line segment between (1,9) and (0, Sx(t) = a + bt ly(t) = c+ dt…

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Q: Let w = 8y dx+ 8x dy+ dz be a one-form on R³. Find a parametric curve a : [0, 1] → R³ such that w =9…

A: The line integral ∫CPdx+Qdy+Rdz involves integration over a specific path. The general form of the…

Q: Consider the smooth parametric curve 6 defined by the equations t (t²-3) { 3 (t²- 3)' = = where t€…

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Q: Match each of the following parametric Equations with a plane curve : x(t) = 3 + 6sinh(t). y(t) = 2…

A: We are authorized to answer three subparts at a time, so we are answering the first three subparts,…

Q: (a) Find the tangent line(s) to the parametric curve given by x(t) = t° – 4t", and y(t) = t. at the…

A: We are authorized to answer one question at a time, since you have not mentioned which question you…

Q: use the given graphs of x = ƒ(t) and y = g(t) to sketch the corresponding parametric curve in the…

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Q: Which is a parametric equation for the curve y = 9 – OA. c(t) = (t, 2 + t) OB. c(t) = (t, 9 – 2t)…

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Q: 3. Let R(t) = (t²,1 - t², t) and r(t) = cost. Determine the parametric equations of the line tangent…

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Q: use the given graphs of x = ƒ(t) and y = g(t) to sketch the corresponding parametric curve in the…

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Q: Consider the curve C given in parametric equations as t(t – 1)2 In (4t² + 1) %3D C : for t e R. (a)…

A: Given problem is :

Q: What is d²y at t = -2? dx2

A:

Q: Q2 - A) Find the parametric equations for the line that is tangent to the given curve : r(t) = (a…

A: To find The parametric equations for the line that is tangent to the given curve

Q: 5. Find the length of the parametric curve x = t + y = v12t +5, 1<t<2. %3D

A: We have to find the curve length.

Q: 2. Consider the parametric curve r = t + 1, y = t - t. dy (a) Find d.r dy (b) Find da?

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Q: Eliminate the parameter f in the parametric equations z(t)=√t+1, y(t) = Sketch the graph of the…

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Q: Find a rectangular equation for the plane curve defined by the parametric equations. x = t + 4, y =…

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Q: 16. Sketch the parametric curve x = Vt, y= sin t, 0<t< 2n. (b) (a) 1.0 (c) 101 1.0 0.5 0.5 0.5 05 10…

A: The graph of the parametric curve x=√t, y=sint , 0≤t≤2π is given as below,

Q: Let w = 8y dx + 8x dy + dz be a one-form on R3. Find a parametric curve a : 0, 1] → R³ such that W =…

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Q: Consider the following two parametric curves in R³: for 0 ¯¯\ND OXO OXO OXO OXÍ These curves…

A: First we will find the intersection point of both server then we will find the equation of potential…

Q: Let C be the parametric curve defined by tan-1t y = } In(1+ t²) where t > 0. dy (a) Find and dx dx2…

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Q: Determine the exact length of the curve for the parametric equation x = tsint and y = tcost for 0 ≤…

A: To find the exact length (arc length) of the curve for the parametric equation x=t sin(t), y=t…

Q: Find of the parametric curve x = sect, y = tant, at t = dx? Select one: -3V3 -1 3V3 3y3 1 3v3 O none

A: Here we find the double derivatives value at t=π/3

Q: Match each of the following parametric Equations with a plane curve : x(t) = - 3t y(t) = 1 - 9t² TER…

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Q: 1. For the parametric equations: x = 4t3, y= 2 +60t – 8t?, find: a) All values of t at which the…

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Q: Suppose parametric equations for the line segment between (7, 8) and (5, 1) have the form: Sx(t) = a…

A: We have to find

Q: Let R(t) = (²,1-t², t) and r(t): = cost. Determine the parametric equations of the line tangent to…

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Q: Consider the parametric equations defined by x(t) = 3t² – 3 and y(t)= 2t +1, for t> 0. d'y at t= 1.…

A: Option A is correct option.

Q: Which of the following gives the length of the path described by the parametric equations r (t) =…

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Q: -2 Find the projection of v = 1 onto the line l of R³ given by the parametric equation l = tủ, where…

A: We will find out the required projection.

Q: [6]. Consider the following set of parametric equations: x = r° - 3t y = 312 – 9 On which intervals…

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Q: A curve C is defined by the parametric equations x(t) = 3 + t“ and y(t) = t° + 5t.Which of the…

A: Given,         A curve C is defined by the parametric equations xt=3+t2 and yt=t3+5t.

Q: Suppose parametric equations for the line segment between (2, 8) and (– 2, 0) have the for s ¤(t) =…

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Q: Match each of the following parametric Equations with a plane curve : x(t) = 3 + 5cos(t), y(t) = 4 +…

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Q: Consider the following parametric curve: x(t) = 3t^2 −6 and y(t) = 3t^4 −3t^2 +12t +10 Find the…

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Q: Find for the parametric curve c(t) (t-1 – 5t, 41) at the point t = -2. dx (Use symbolic notation and…

A: Given problem:- Find dy/dt for the parametric curve c(t) = (t-1 - 5t, 4t3) at the point t = −2.

Q: Which is the graph of the derivative dyldx of the parametric equations x(t)= 3cos t and y(t)=3sin t…

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Q: - Let C be the curve in R parameterized by r(t) = (t², t³, t^). (a) Compute r'(1). (b) Find a…

A: Given; r(t)=&lt;t^2,t^3,t^4&gt;

Q: 1. Consider the graph of r(t) = 2t i+ tj +t° k Determine parametric equations of the tangent line to…

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Q: Find the length of the parametric curve C {(x(t), y(t)) : t E 1} x(t) 4cos(t), y(t) = 4sin(t), with…

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Q: - (2e'cos t) i+ (2e'sin t)j 7K Find T, N, and k for the space curve 7k.

A: Given,           The space curve is rt=2etcosti+2etsintj+7k.To find : Find, T, N and k for the given…

Q: iven R'(t) = (4e²t, 2t ,2cosh t), and R(0) = (1, −2, 3), 1+t² find Ŕ(t), and give the parametric…

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Q: 1 '1+t²⁹ Given R'(t) = (4e²t, , 2cosh t), and R(0) = (1, -2,3).

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Q: 2. Consider the curve C given in parametric equations as t(t – 1)2 In (4t2 + 1) C: for t e R. (a)…

A: Tangent and normal line

Q: 11. C is the curve F(t) = (In (2 – t), V+3). Find parametric equations for the tangent line to C at…

A: According to question,Given Curve C,Ft = ln2-t, 1t-2, t+3

Q: " | and F(x.y) = <y-x, x+3), then TE If C is the curve parametrized by 7(1)= <2sint, 2cost), te 0,-…

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Q: Find the length of the curve C defined parametrically by C:x(t) = e' cos t, y(t) = e' sint, 0<tS#…

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