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

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 an equation for the line tangent to the curve at the point defined by the given value of t. x-…

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Q: Find the length L of the curve R(t) = e* cos(3t) i + e* sin(3t) j + 3e*k over the interval [1, 5]. L…

A: given: Rt=etcos3ti+etsin3tj+3etk interval 1,5

Q: 1. Find the length of the curve given by e' (sin t+cos t) , yY = e'(cos t – sin t), x = 1<t< 4 .

A: The length of a parametric curve is given by L=∫abx't2+y't2dt Now, we have…

Q: What is the point of intersection of the tangent lines to the curve r(t) = sin(πt)i + 8sin(πt)j +…

A: Let us consider the given curve r(t) the tangent line is obtained as Find the derivative of the…

Q: Find the length of the curve. r(t) = cos(2t) i + sin(2t) j + 2 ln cos t k,     0 ≤ t ≤ π/4

A: Consider the length of the curve is, r(t)=costi+sintj+(lncost)k Then,…

Q: Find the length of the following curve: y = ln(cos(x)) from x=0 to x=pi/4

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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: - Sva cos 2t dt from x= 0 to x= Find the length of the curve y =

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Q: Find the arclength of the curve a = 8 cos(3t), y = 8 sin(3t) with 0 < t<. 9

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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 T', N and B for the curve r(t) = (2 cos(5t), 2 sin(5t), 4t) at the point t = 0

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Q: Consider the parametric curve: x = sin² (t) y = -9t Which integral gives the arc length of the curve…

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Q: 5. Find an equation of the tangent to the curve at the point corresponding to the given value of the…

A: The given parametric equations are, x=t3+cosπt, y=4t+sin2t+6. Find the equation of the tangent to…

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

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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: 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: A particle moves in the xy-plane in such a way that its path is defined by x = e^t cos t and y = e^t…

A: Given that, x = e^t cos t y = e^t sin 2t Differentiating x with respect to t we get, dx/dt = e^t cos…

Q: Find the length of the curve 7(t) = (cos(4t), sin(4t), 5t) for – 8 <t< 1 Give your answer to two…

A: use the arc length formula for finding length.

Q: A) Find the distance traveled by a particle with position (x, y) as t varies in the given time…

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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: 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: 8. Find the length of the curve defined by x = cos(2t), y = sin(2t) from t = 0 to t = n.

A: If x = f(t), y = g(t) in (a, b) then length of the curve is,

Q: 1. Find the length of the curve r(t) = (sin 2t, cos! cos 2t) from t =0 to t 2n. %3D II

A: 1)- Given: r→t=sin 2t, cos 2t from t=0 to t=2π. The objective is to determine the length of the…

Q: Q1. Find the length of the of the curve y = In(cos x) from x = 0 to x = 4

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Q: 1. Find the length of the curve r(t) = (sin 2t, cos 2t) from t 0 to t= 2n. CoS %3D

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: computes curve length for 0

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

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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: Find the lengthof the curve r= a sin² (0/2), 0 s0s T, a>0

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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 distance traveled by a particle with position (x, y) as t varies in the given time…

A: Given : x = cos2ty = cos t0 ≤ t ≤ 4π

Q: Find the arclength of the curve z = 7 cos(3t), y = 7 sin(3t) with 0 < t< 12

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Q: Find the length of the curve x = 8 cos t + 8t sint,y= 8 sin t – 8t cos t ; 0 < t %3D -

A: The length of the parametric curve is given by  L=∫abx't2+y't2dt.

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: Consider the parametric curve: X = sin² (t) y = -9t Which integral gives the arc length of the curve…

A: Topic = Integration

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

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Q: 7. Find the length of the curve f(1) = In(sin r), 0 < r < a/6.

A: Topic = Application of integration

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: Consider the parametric curve: X y = ln(-t) Which integral gives the arc length of the curve over…

A: We have to find the length of curve.

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: Consider a curve parameterized by: c(t)=(sin^3(t),cos(t)) Compute dy/dx at the point ((sqrt(2)/4),…

A: Differentiate the given function as follows.

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: 1. Find the arc length of the curve f(x) = 3 4 (x + 2)2 on the interval [0, 4]. 3

A: Find the arc length

Q: Find the arclength of the curve x 5 cos(8t), y : 5 sin(8t) with 0 <t <

A: Given: x= 5cos8t  ; y = 5sin8t     with 0≤t≤π8---------------------Aim: To find the arc lengthL of…

Q: The position of a particle in the xy-plane at time t is given by r(t) = (cos 2t) i+ (2 sin 2t) j…

A: Given: rt=cos2ti+2sin2tj For finding equation in x and y whose graph is the path of the particle, we…

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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Q: Q1. Find the length of the of the curve y = In(cos x) from x = 0 to x = . %3D

A: Explanation of the solution is given below...

Q: Find the arclength of the curve æ = 5 cos(4t), y = 5 sin(4t) with 0 < t s 4

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Q: Find (2x + xy)ds, where C is the arc of the curve y = sin (x) for 0 ≤ x ≤ π

A: The given problem is to evaluate the given line integral of the given function over the given curves…