Find the are rength of the curve whose paraumetric equations are : Jfd ad S x=COS2E +2bsin 2t E59 51 9250972-72ui5 -h 2 3951 -2sinzt + 2sinzt + 1t cos 26 :4t cost 14-2 Cos Zt -2cos2t +4tsin2E dx %3D dt Vilet (sin'2t + cos*2t) 2(3)' - 2(0) " %-D 1७

Q: Let C be the curve parameterized by r(t) = (cos(t), sin(t), /3t), 0 <t < 1/2. Calculate 1. |r'(t)| =…

A: Given:- r(t)=&lt;cos(t),sin(t),√3t &gt;   To find:-

Q: Find the orthogonal trajectories for the family of curves, sin? y C In x.

A:

Q: The length of the curve defined parametrically by: x = e*cost, y = e' sint, 0 Sts is equal to:…

A:

Q: Find an equation of the tangent to the curve given by = evi y = t – In(?) at the point corresponding…

A:

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: (b) Consider the curve C with parametirzation 7(t) = (5 cost, 5 sin t, 500), where 0 <t< 27. Let F =…

A: We have,

Q: If 2 Bézier curves are joined at the point p3 what is necessary for C' parametric continuity? O A.…

A: Given: 2 Bezier curves are joined at the point p3. To explain what is the necessary for C1…

Q: ind a parametrization for the ray (half line) with initial point (2,3) when t=0 and (-1,0) when…

A:

Q: e-param

A: Here we have,  ex+e-y=c ................(1)  differentiate with respect to x

Q: Find an equation for the tangent line to the curve given parametrically by x(t) 2t, y(t) 4t2 +t+ 3 =…

A: we want to find the tangent lines to theparametric equations given byx=f(t)  y=g(t)The equation of…

Q: . Sketch the curve parametrized by r(t) = (ltl + t, ltl - t)

A: The given curve is rt=t+t, t-t. Sketch the graph of the above curve as shown below.

Q: Show that the exact length of the curve below is y = Vr - r² – sin ¬1 (V7)

A: SOLUTION-

Q: the detined b is Constant. Curiature a(t) =| 1 Cost, 1 sint, o of the curve d:laa)tR? where Find

A: We are given : α(t)=1rcos t,1rsin t,0 ⇒α'(t)=-1rsin t,1rcos t,0 Now, the Unit tangent Vector is :…

Q: YouTrylt 4 Consider the path of a particle given by tangential and normal components of acceleration…

A: The position vector of the particle is given by  r(t) = 2t2, t3, -1

Q: ) Find the orthogonal trajectories of the family of curves r = 3C sin 0, where C being parameter.

A:

Q: The parametric equations of a curve are given by x = In (VE +1) and y = cosh-' (2t). dy when t = 1.…

A: Given x=lnt+1 and y=cosh−12t We have to find the dydx when t=1 We know that dydx=dydtdxdt.....1…

Q: The length of the curve defined parametrically by: x = e*cost, y = e'sint,0 <t <, s equal to: Select…

A: tea

Q: Find the slope of the tangent line to the parametric curves x=3t+2, y= 2t^2+ 3t-3 at t=11 and then…

A: The given question as belonging to the derivative in which we have to find the derivative or the…

Q: Find the value of Jsinydx+ (xcosy-siny)dy, where Cis any curve from (2,0) to (1,n). Ca.2 Cb1 none of…

A: Green's theorem: ∫C Pdx+Qdy =∬D ∂Q∂x-∂P∂y dA where P and Q have continuous first order partial…

Q: Find 4 and 4y axz dx y=te* dy- -(t-1)et y t is Fov which values the curve con cave upwavd. U BRANDS

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Q: Find the equation of the tangent line to the parametric curve at (1,3). 2=1+ Int y =t² +2

A:

Q: Find the tangent line(s) to the parametric curve given by a = t5 – 4t3 y = t? at (0, 4).

A: Find the tangent line(s) to the parametric curve given by x = t^5-4t^3 , y = t^2 at (0,4).

Q: Find the tangent line(s) to the parametric curve given by a = t-9t and y =t at (0, 9) %3D %3D

A: We have to find the tangent line

Q: Find the vector equation of the tangent line to the curve given by 7(t) = sin ti + cos (2t)j + tan…

A: There is no such introduction for the solution.I have explained it within the solution.Please go…

Q: Use Green's Theorem to evaluate | F. dř, where F = (Va + 4y, 2x + 9) C consists of the arc of the…

A:

Q: 5. Find the length of the curve given by y= Vt* – 1 dt and 1<x<2.

A:

Q: Which of the following is an arc-length parametrization of the line segment from (2,1) to (1,3)?…

A: We will find out the required value.

Q: Find the speed of the cycloid c(t) = (4t − 4 sin t, 4 − 4 cost) atpoints where the tangent line is…

A: Given: c(t)=4t-4sin(t), 4-4cos(t)

Q: Find a parametrization of the tangent line at the point indicated. r(t) = (1 - t4, 4t, 5t), t = 2…

A:

Q: Find a parametrization for the line through the point (a, b) having slope m.

A: Given that slope = m , this can be written as &lt;1,m&gt; vector. And point= (a,b)

Q: The parametric equations of a curve are given by x = In (VE +1) and Vt + y = cosh-(2t). X = dy when…

A:

Q: Let C be the parametric curve given by 1²+2t +8, C: y= cost +1, An integral for the area of the…

A: Given parametric curve is,

Q: Consider the parametric curve: x = 5t² y = 2et Which integral gives the arc length of the curve over…

A:

Q: Find the length of parametrized curve given by x(t)=−6t^2−6t,y(t)=−4t^3−6t^2 where t goes from 0…

A: Given information:  The parametric equations are x(t)=−6t2−6t,y(t)=−4t3−6t2 over the interval .0≤t≤1…

Q: Obtain the gradient to a curve with the parametric equations given by I = In - and y = sinh 2t whent…

A:

Q: The curvature of the curve 7 (t)={2t, 2t+1, sin2t) at t= is 4 O 1 O 1 O 2 1/818 1/2

A: Here the given curve is r(t)⇀ ==(2t,2t+1,sin2t) Here we have to find the curvature of the curve at…

Q: Determine the length of the parametric curve given by r = 2t3, y = 3t² where 0 <t<V8. %3D CS Scanned…

A:

Q: Find the length of parametrized curve given by x(t)=12t^2−12t, y(t)=−4t^3+6t^2+9t where t goes…

A: Let us consider the parametrized curve x(t) and y(t)  The length of the curve is obtained as…

Q: Find an equation of the tangent(s) to the curve with paramnetric equations ¤ = 1+ VE, y = e" at the…

A:

Q: Consider a curve C in guen by r(t) = / 7t-Sin(F) cas(t), 4t, -2cos (+)) with Oste5 Verify that ri(t)…

A:

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

A:

Q: Find the equation of the tangent line to the curve y = et at the point (0, 1). Give your answer in…

A: Given,            The curve is y=exx2+1 and the point is 0,1.To find : Find the equation of the…

Q: find the Cerrvature of the Curve x:(0,1|R? defined by x(t)=14Cost, 1sint,o), where %3D is coostant 2

A: α(t)=(1rcost ,1rsint ,0)r is constantTo find the curvature of the given curve

Q: Find the length of parametrized curve given by  x(t) = 6t2 + 12t, y(t) = -4t3- 12t2 - 9t where t…

A: Consider the parametric curve given by: x(t)=6t2+12t and y(t)=-4t3-12t2-9t for t from 0 to 1. The…

Q: Consider the parametric curve segment (t, t2), t ∈ [0, 1]. What is the firstorder derivative of the…

A: We have the given parametric curve t,t2, t∈0,1x=ty=t2 for t∈0,1the first order derivative the curve…

Q: Find the orthogonal trajectories of the family of curves r 5C sin 0, where C being parameter.

A: Follow the below steps to find the orthogonal trajectories. Differentiate the function with respect…

Q: Calculate S. xydx + 3y*dy where C is the curve in xy plane, x = y² from (0,0). to (1,3).

A: We have to calculate the integral ∫Cxydx+3y4dy Where C is the curve in the xy plane, x=y2 from 0,0…