Find f F. dr for F = 2yi – (sin y)j on the curve counterclockwise around the unit circle C starting at the point (1,0). ScF• dř =

Q: For the function y = d + a cos(bx − c), d represents a ________ ________ of the basic curve.

A: For the function y = d + a cos(bx - c), d represent a ............... of the basic curve.

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

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Q: 4. Find the moving trihedral of the curve f(t) at the indicated value: †(t) = cos? t î + sin² t ĵ…

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Q: Find fe F dr for F = 7yi - (sin y)j on the curve counterclockwise around the unit circle C starting…

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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: Consider the graph of f(x, y) = excos(xy²). Find an equation of its tangent plane at (0,0, 1) and…

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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: 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: 8. Given the space curve r(t) = (sin²t, cos't, tant), find an equation of the tangent line in…

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Q: The slope of the tangent to the curve r = 3 sin 40 at 0 = 0 is %3D Şelect one: O a. -1 3D1 O b. 0 C.…

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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: 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: The curves C,:x=t, y=t, z=t, t20 and C,: x= sint, y 1+cost, z=1, 120 have intersection at the point…

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Q: Find Sc F · dr for F = 3yi – (sin y)j on the curve counterclockwise around the unit circle C…

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Q: Sketch the following curves 2. y = sin(x) + v3 cos(x) on [–27, 27].

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Q: Find the condition that the line x cos a + y ain a =p may touch the curve yh =1. am bm

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Q: Find the arclength of the curve r(t) = (2 sin t, 6t, 2 cos t), –7 < t < 7

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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 unit tangent of the following curve at the specified point. r(t) = 2ti + 1 · sin(2t)j+3 ·…

A: We have to find the unit tangent vector at t=pi/3

Q: Find the exact length of the curve. 43. x = t sin t , y = t cos t , 0 ≤ t ≤ 1

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Q: Find the speed (as a function of t ) of a particle whose position at time t seconds is c(t) = (sin t…

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

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Q: Find ſo F · dr for F = 8yi – (sin y)j on the curve counterclockwise around the unit circle C…

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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: where C is the curve r(t) = (sin(t), cos(t), sin(2t)), 0 ≤ t ≤ 2

A: Given C is the curve                        r(t)=sin(t), cos(t), sin(2t), 0≤t≤2π and…

Q: Let C be the curve parameterized by Y: [0, b] R³, y(s) = (12 cos(s²), 12 sin(s), 9 s²). Find b>0…

A: The given problem is to find the value of b for which the given length of curve of the given…

Q: Find the length of the curve. r(t) = cos(4t) i + sin(4t) j + 4ln(cos(t)) k,  0 ≤ t ≤ ?/4

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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: Find the angle between the tangents to the curve R(t) = ti + 2tj – t°k at the points t = +1

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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: Graph the Plane Curve defined by: I = 3 cos(t) - t + 5. y = sin(t). for t in [0, 37]. x Clear + Undo…

A: Plot the points for different values of t from [0,3π]. Draw the curve passing through the points.

Q: Find the maximum, minimum and inflection points of the fur y= 3 sin 2x at [0, T].

A: Solution:-

Q: Find T, N and B for the curve F(t) = (2 cos(5t), 2 sin(5t), 3t) at the point t -0 Give your answers…

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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: The parametric form of the tangent line to the image of f(f) = (4i², 2,t – 3) at t = 2 is L(t) =

A: To find the parametric form of the tangent line to the image of f(t)

Q: Find the length of the curve 7 (t) = (4 cos(t), 4 sin(t), 3t) for – 1 <t< 4

A: Here we have to calculate arc length in given interval.

Q: Find the length of the curve. r(t) = cos(5t) i+ sin(5t)j + 5ln(cos(t)) k, 0<t< n/4

A: r(t)=cos(5t)i+sin(5t)j+5ln(cos(t))kWhere, 0≤t≤π/4

Q: Find the arclength of the curve y=3/2x^2/3 for x=1 to x=8.

A: Find the arclength of the curve y=3/2x^2/3 for x=1 to x=8.

Q: The parametric form of the tangent line to the image of f(t) = (5t², 2,t – 2) at t = -1 is L(t) =

A: Topic = Application of derivative

Q: Find an interval of t-values with t > 0 such that c(t) = (cos t, sin t) traces the upper half of the…

A: Given,  ct = cost, sint  and t ≥ 0 We have to find the interval of t-values such that ct = cost,…

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​ three-dimensional curve. r(t)=cos t, sin t, 3t​, for 0≤t≤2

A: Given that rt =cost,sint,3t  for 0≤t≤2 find the length

Q: (a) Find the point of intersection of the tangent lines to the curve r(t) = (sin 7t, 2 sin Tt, cos…

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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: Consider the following. x = 3 cosh(t), y = 2 sinh(t) (a) Eliminate the parameter to find a Cartesian…

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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: The parametric form of the tangent line to the image of f(t) = (2t², 3, t - 1) at t = 4 is t L(t) =

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Q: Find the length of the curve defined by the following function for 0 <t < 2n. 7(t) = (– cos 2t)i +…

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Q: Find the speed of the curve F(t) = (4cos (t), 4 sin(t), 6t) at t = 3 %3| Speed =

A: Consider the curve  r(t)=&lt;4cost2,4sint2,6t&gt;