Prove that the curve r(t) = (a cos t,b sin t,.csint is parameterized by length provided a=b2 +c² = 1. arc ..... Begin by calculating r'(t). r'(1) = {COD

Q: Find the arclength of the curve z 9 cos(9t), y = 9 sin(9t) with 0 <t< 36

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Q: Find the exact slope of the tangent line to the 4 cos(t) parametric curve at the point ly = 7 sin(t)…

A: To Determine: Exact slope of the tangent line to the parametric curve :

Q: 7. Find the length along the parametric curve defined by v(t) = (t, In(cos(t))) from t = 0 andt=.…

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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: 2. Write an arc length parameterization for the curve r(t) = cos ti + sin tj + 3t k ; 0<t

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Q: Find the length of arc of the given curve. 5. R= (sin 2t , cos 2t , 2t³/2), 0 sts1.

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Q: Consider the curve C shown in the figure, parameterized by: C: r(t) = (1 - cos(t), 1- sin(t), 1 +…

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Q: find y'' for the curve cosx-siny=4

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Q: Find arc-length of the following curve 0 <t < 2 x = sin (t) Y = cos'(t)

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Q: 23. Find the unit tangent vector T and the curvature k for the following parameterized curve. r(t) =…

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Q: Sketch the plane curve r(t) = a cos3 ti + a sin3 tj and find its length over the given interval [0,…

A: The curve is r(t)=a cos3ti + a sin3tj   Interval is 0, 2π

Q: 2. Given that r(t) = 2 sin ti + 2 cos tj+ tan tk. Find the unit tangent vector T(t) at the point…

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Q: A curve is defined by the parametric equations: x(1) = e' cos t, y(t) = e' sint d²y dy and dr of the…

A: It is given that, x(t)=et cost,y(t)=et sint   It is known that, dydx can be found by chain rule and…

Q: Find the arclength of the curve y = * - In x if < y s-1. Do not simplify your answer for this…

A: Given: y=18x2−lnx18≤y≤e28−1

Q: Parameterize the curve r(t) = (2+ cos 3t, 3 – sin 3t, 4t) using arc length, s, as a parameter. Use t…

A: Given the curve rt=2+cos3t, 3-sin3t, 4t---1. Differentiating, we get vt=r't=-3sin3t,…

Q: Consider the curve C parametrized byx = −1 + 6 sin t and y =(1/2)− 6 cos t for −π ≤ t ≤ 7π. What is…

A: First of all, consider the given parametrized equation of curve C. Rearrange the equations to write…

Q: Find the speed of the cycloid c(t) = (2t – 2 sin t, 2 – 2 cos t) at points where the tangent line is…

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

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Q: Consider a new curve Č parametrized by r(t) = (cos t esint, sin t- cos t), 0 <t <I but with F still…

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Q: Find an equation of the tangent(s) to the curve with parametric equations tsint at the point…

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Q: Given: smooth curve C parametrized by Ř(t) = 8. Cos tv2 8 sin 3 1. Find the unit tangent, unit…

A: Given

Q: 4. Find the radius and centre of curvature of the curve x = (1 - at) cos t + a sin t, y = (1 – at)…

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Q: Find the length of the curve x=1+2sin at, y=3–2 cos at, 0<t<l

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Q: Compute the arc length of the indicated portion of the curve: 7(1) = (7 +2r²)î + (21² – 4)ĵ + (7 –…

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Q: Determine the intersection point of the lines tangent to the curve r (t) = (senπt, 2senπt, cosπt) at…

A: The given curve is rt=sinπt,2sinπt,cosπt. Differentiating it with respect to t:…

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

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Q: 3. Reparametrize the unit tangent vector T(t) using the arc length as parameter starting from t = 1.

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Q: Find the tangent line(s) to the parametric curve given by a = t¹ - 9t² and y=t² at (0, 9).

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Q: The parametric curve x(t)=t−2t6 and y(t)=t7+2t2 is given. In which case is the tangent line at the…

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Q: Consider the curve where a =0 (a) Compute(t) at t = [0, +∞). (b) Find the tangent line at the point…

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Q: If the arc length s of the curve C:r (t) = cos(t)i + sin(t)j+ 3tk from t 0 to t = bis 20 units, then…

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Q: Consider the following. x = sinh(t), y = cosh(t) (a) Eliminate the parameter to find a Cartesian…

A: Solution: The objective is to eliminate the parameter to find a Cartesian equation of the curve

Q: Calculate the length of the curve r=a*sin(^3)(x/3) for (x(1)=0, x(2)=3pi)

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Q: Find the length of the following curve using methods for parametric curves. x = 4 sin t y = 4 cos t…

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Q: Find the length of the arc of the curve having the parametric equations x = t³3 and y = from t = 0…

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Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

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Q: Find the length of arc of the given curve. 5. R= (sin 2t, cos 2t , 2t³/2), 0 sts1.

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Q: In which direction is the curve x = -2 sin t, y = 2 cos t, for 0 ≤ t &lt; 2π, generated?

A: x = -2 sin t, y = 2 cos t Table for values of x and y: t x y 0 0 2 π 0 -2 π2 2 0 2π 0 2

Q: From Rogawski ET 2e section 8.1, exercise 11. Approximate the arc length of the curve y = i x4 over…

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Q: Consider the curve r=[(e^(t))*cos(3t), (e^(t))*sin(3t), e^(t)] Compute the arclength function s(t):…

A: The arc length function is given as: st=∫atr'tdtrt=etcos3t,etsin3t,et  with initial point 0

Q: Consider the curve C parametrized by(x, y) = (5 cos (−12t), 5 sin(−12t)), for −π/2 ≤ t ≤ π/2 What is…

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Q: Calculate the length of the curve γ (t) = (cos(2t), sin(2t)) t ∈ [0, π].

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Q: 2. Determine whether the following curve uses arc length as a parameter. If not, find a description…

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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: Consider the curve y = – In|cos(x)| as x travels from T to 6 a) Find the length of the curve.

A: Hi, since you have asked multiple questions, we will solve the first question for you. If want any…

Q: Find the lengthof the curve r= a sin (0/2), 0s 0S T, a>0

A: The formula for finding arc length is L = ∫0πr2+ drdθ2dθ, where r = a sin2(θ2)

Q: Calculate the arclength of the following curve on the given interval. y%=2x3/2+1O on the interval…

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