Find of the curve the curve lenght from t=o to t=2M given C: P(t) = (cos 3t) î + (sin 3t) Î + ? tVt k 3.

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

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Q: Consider the following. tan2(0), y = sec(0), -n/2 < 0 < t/2 X = (a) Eliminate the parameter to find…

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Q: Find T, N and B for the curve r (t) = (4 cos(5t), 4 sin(5t), 5t) at the point t = 0 Give your…

A: Find T→,N→ and B→ for the curve r→(t)=4 cos(5t),4sin(5t),5t at the point t=0give your answer to two…

Q: Find the exact length of the curve (b) x = e' cos t, y= e' sint, 0<t<T

A: Length of the curve for parametric equation is given by:

Q: Find the moving trihedral of the curve 7(t) at the indicated value: 7(t) = cos? t î + sin? t ĵ + 1…

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Q: Find f F. dr for F = 2yi – (sin y)j on the curve counterclockwise around the unit circle C starting…

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Q: 2. Find the length of the curve 0<t< 2n. r(t) e'i + e' sin 2tj + e' cos 2tk,

A: From the given problem :   rt=eti+etsin2tj+etcos2tk   So,   x=et, y=etsin2t , z=etcos2t .   As we…

Q: find the arclength of the curve r(t)= , -7<t<7

A: NOTE: Refresh your page if you can't see any equations. . take derivative

Q: II. Find the length of the following curves. (a) x = 2t , y = cos 4t, 0 <t <

A: Given:    x = 2t    y = cos4t    0 ≤ t ≤ π/2

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: Plot the curve c(t) = (cos t, esin t ) for 0 ≤ t ≤ 2π

A: The plot of the curve for t within 0 to 2pi is shown in figure below.

Q: Find the length of the given curve: r(t) = (-3t, -3 sint,-3 cos t) where-3 sts 5.

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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: 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: Prove that the curve y:(-,) → R³ is regular with factor H and determine whether the image y (t) = (2…

A: To determine : the      included in a plane in   or not. Here,…

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: Find the length of the following two-dimensional curve. r(t): = (cos t, sin t) , for 0stsT The…

A: The formula for finding the length of the curve is explained in step 2 with a general observation…

Q: Prove that the curve y: (-,-)→ R³ is regular with factor H and determine whether the image y (t) =…

A: If γ't not equal to 0 for all t∈-π2,π2then it is regular. If γ''t=kγ't for all t∈-π2,π2 then the…

Q: Find the length of the curve. r(t) : cos(8t) i + sin(8t)j + 8 In(cos(t)) k, 0 stS T/4

A: Solution is given as below:

Q: Find T,N and k for the curve: 1- r(t) = (6 sin 2t)i + (6 cos2t) j+5tk.

A: As per our guidelines we are supposed to answer only one question at a time. Kindly repost other…

Q: Find the arclength of the curve below over the interval -1<t<1

A: Here we have to find the arc length of the given curve.

Q: Find the arclength of the curve r(t) (6 sin t, 2t, 6 cost), -2 < t <2

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Q: A particle P moves on the curve r= 3i + 4t²j. The distance of P from the origin when t =1 is

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Q: What is the slope at t = −2 ?

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Q: Consider the curve r(t) = (t, 3 cos t, 3 sin t) for t 2 0. Find an equation for the projection of…

A: Equation of projection of curve on xy plane will not contain the term of z.

Q: Find the exact length of the following curve y = Vx – x² + sin-'(/T).

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Q: Find the length of the following two-dimensional curve. r(t) = (2 cos t,2 sin t), for 0stsT

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Q: The length of the curve r(t)= [cos(t), sin(t), – 3t]with 0 <t<2n is equal to O A. 2/5 T O B. 2/6 T O…

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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: 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: 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: For the curve x=3cos(t), y=4sin(t), find the value of d^2y/dx^2 at the point where t=π/5.

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Q: 3. For the curve x – xy² = 8e²4, do the following | a) Verify that the point (2,0) is on this curve.

A: Given, curve x3-xy2=8e2y

Q: A curve C has parametric equations X = tチ+1. dy (i) Find in terms oft. dx (ii) Show that there are…

A: We first find dy/dx

Q: Consider the curve r(t) = (t, 3 cos t, 3 sin t) for t 2 0. Find an equation for the projection of…

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Q: A curve is written parametrically with x and y defined as functions of t: x=t2 +1, y = 4r° +3. Find…

A: Take the derivative of x and y with respect to t then use the formula for the arc length.

Q: Let Sketch the curve and find the length of this curve. r(t) = (t, 3 cost, 3 sin t), 0≤ t ≤ 2π.

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Q: Given the parametric equation x=(4/5)t5/2 and y= (1/4)t4-t find the arc length of the curve on the…

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Q: Find the length of the curve. r(t) = cos(3t) i + sin(3t)j + 3 In(cos(t)) k, 0 <t< n/4 %3D

A: Find the length of the curve:…

Q: Find the length of the following two-dimensional curve. r(t) (2 cos t+2t sin t,2 sin t- 2t cos t),…

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Q: Find the curve lenght from t=o to te2T of the given curve C: P(E) = (cos3t) î + (sin 3t) Î t ? tJE e…

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Q: Find the length of the following three-dimensional curve. r(t)= (sin t, cos t, 2t), for 0sts4

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Q: Find the derivative 4cos4t sin4t O2cot4t O Other: -1/2 cot4t of the parametrically defined curve (t)…

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Q: d'y Find for the curve given by x= sin 2t and y = cos 2t. %3D %3D (a) 8 sec (2t) tan(2t) (b) -8sec…

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Q: 2. Let y be the curve in R3 given by t (t, 2 cos t, 2 sin t) for 0 <t < 47. Compute ds

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Q: Find the length of the following two-dimensional curve. 兀 r(t) = (9 cos t + 9t sin t 9 sin t-9t cos…

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Q: Find the length of the curve r(t) = (cos(3t), sin(3t), 4t) for -6 ≤ t ≤ 5 Give your answer to two…

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Q: For the curve with parametric equations x = 4 sin (t) – 1 y= 2 cos (1) + 3 dy find the point dx at…

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Q: Find F. dř for F = 5yi – (sin y)j on the curve counterclockwise around the unit circle C starting at…

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