Evaluate the line integral f, F . dr, where C is the curve given by F(t) = 3 cos ti+ 3 sin t j, 0

Q: dy ecos (2t). Find an expression for -for Consider the parametric curve x (t) = -esin (3t) and y (t)…

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Q: Solve the initial value problem for transverse vibration of a taut string of length L which is…

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Q: Find X || d'y dx² t' Od²y dr² = for the following parametric functions. y = √t 43/2 4 015/2

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Q: 8. For the curve given by r(t)=√√² +8 i + In(t² + 8)j + tk 2 find: a. r'(t)

A: Introduction: For a vector curve rt=ati+btj+ctk, the tangent line at the point of contact t=t0 is…

Q: Evaluate the line integral (2 yi + (r- 2)j+ zyzk) · dr where C is the parametric curve r(t) = ti +…

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Q: Consider the parametric curve x(t) a) Sketch and identify this curve. b) Set up an integral to…

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Q: c) A curve has a parametric equation x = 2t - 1 and y = t* -t'. dy Evaluate dx? 1 at t = 2

A: Given, The parametric equations x=2t3-1, y =t4-t3.

Q: Let C be the parametric curve defined by x(t) = t²-t-6, [y(t) = 4t³ + 3t² − 6t. a. Determine the…

A: Given: xt=t2-t-6yt=4t3+3t2-6t To find: a) Horizontal tangent line b) Definite integral

Q: Let fcxry)= 2X sinly)+3X Cos CY ). Find the tangent Plane at the point 2,0).Use the tangent Plane to…

A: In this question, concept of tangent plane at any point is applied. Tangent Plane Naturally, it…

Q: ind the length of the curve x cos(t) + In(tan(;t)), y = sin(t), /4<t< 3n/4. %3D ength =

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Q: = Let x: R? → R³ be the function given by x(u, v) = (u cos v ,u sin v , bv) 1. Check whether x is…

A: (1)Given that:x:R2→R3 is the function given by x(u,v)=(ucosv,usinv,bv)In order to check the proper…

Q: Find the length L of the curve R(t) = e" cos(2t) i + e* sin(2t) j+2e"k over the interval [1, 4]. L =

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Q: Q: Find the condition that the line x cos a +y sin a = p may touch the curve x"y" = a™*".

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Q: Find the solution u (x,t) to the partial differential equation using the method of separation of…

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Q: Let C be the curve defined parametrically by x (t) = cos (t), y (t) = sin (t) and z (t) = 3t, where…

A: The given integral:∫CF.drWhere Fx,y,z=x2+y2,2yx,z227And the curve C is given by:xt=cos t ; yt=sin t;…

Q: Use Green's Theorem to evaluate | F. dr, where F = (Va + 5y, 2x + Vỹ ) and C consists of the arc of…

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