Find S, F· dř tor F = -5yỉ + 4x} – 4zk if C is the helix x = cos t, y = sin t, z = t, for 0 < t < 4n. ScF· dr = %3D

Q: Find the arc length of the graph by partitioning the x-axis.   9y2 = 4(1+x2)3 , from x=0 to x=4√2…

A: Given: 9y2=4(1+x2)3  from x=0 to x=4sqrt(2)

Q: Find the arc length of the catenary y = coshx between x 0 and x = In4.

A: we'll allow providing one solution at a time. Please submit the rest questions separately.   Given:…

Q: Find Equatien of the tavgnt lin tu th cuve at tk giver pointe y= sec X ,

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Q: The arc length of the curve r= cos 30 with 0<0<nis попе J V-9(sin 30)² + (cos 30)² d0 I (sin 30)² +…

A: In this question we have to find the arc length of the curve.

Q: Consider the helix r(t) = (cos(4t), sin(4t), –2t). Compute, at t

A: Compute unit binormal and curvature at t=pi/6

Q: Find the points on the cardioid r = 1−cosθ at which there is a horizontal tangent line, a vertical…

A: Consider the given: r=1−cosθWrite the cartesian…

Q: Find the arc length of y=((x^3)/6) + (1/(2x)) with the interval of [(1/2), 1].

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Q: What does the arc length formula give for the length of the line y = x between x = 0 and x = a,…

A: line y = x between x = 0 and x = a

Q: calculate the arc length over the given interval. y = 4x − 2, [−2, 2]

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Q: 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. 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 arc length of y^3 + y = x^2 + 6x on the interval [−5, −1]

A: “Since you have asked multiple questions, we will solve the first question for you(Only finding arc…

Q: 8. Find the arc length of y' + y = x² + 6x on the interval [-5, – 1). 9. Using the same arc in…

A: Arc length is the distance between two points along a section of a curve. Formula for finding arc…

Q: If z=x+ iy=r(cos(0) + isin(@)) then |:|=/x? +y² =rO arc z=0 Z=rO

A: By definition of modulus u got |z|=r

Q: Suppose that a particle following the path (e' cos(t). sin(), ) flies off on a tangent at lo = 2.…

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Q: The length of the curve y = In(sec x ) ,from x = 0 to x=n/4 Select one: O In|sec(Tt/4 )| O…

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Q: The value of cosh(3z+1)dz, where C is the line segment from z=1 C to z= 2i. O a. (-sinh(6i+1)+sinh…

A: We have to find the value of integral,  I = ∮Ccosh(3z+1)dz  ;  where C is the line segment from z=1…

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: 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: 2. Find the length of arc of the curve x = + from the point where y = 1 to the point where y = 2. yª…

A: Explanation of the answer is as follows

Q: Find the Arc Length of y= 3ln(x) - ((x2)/24)) on [1,6]

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Q: From Rogawski ET 2e section 8.1, exercise 7. 3 Calculate the arc length of y = x 7 over the interva…

A: use arc length formula for finding it.

Q: Find the arc length of the curve 2sin²(4) from 0 = 0 to r = A = T. Select one: O 4 O 5 O 6 O 7 O 8

A:

Q: Find the arc length of the curve y = 2/3x 3/2 from (1, 2/3) to (2, 4/ 3).

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

Q: 4. Given that r(t) = cos ti + sin tj + In cos tk Find the curvature k and vec- tors T, N, B at the…

A: Find curvature at t=1

Q: Use Simpson’s Rule with n = 10 to approximate the length of arc of r(t) = t i + t2j + t3k from the…

A: Given,

Q: The arc length of the curve r= cos 30 with 0<0 < is T V(sin 30)² + (cos 30)² do 0. o" V-9(sin 30)² +…

A: Given that: r=cos3θand  0≤θ≤π

Q: Find arc length of vactor  valued function r(t)=ti+4tj+3tk over(0,1)

A: r(t)=ti+4tj+3tk over(0,1)

Q: 2. Reparametrize R using the arc length as parameter from the point P(-1, √37,5).

A:

Q: Compute ž dz +y1 z dz, +72 and where +Y1 is the segment from 1 to -1, and +y2 is the arc on the unit…

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Q: Evaluate the line integral | (x + 3y + )ds, where Cis the line segment joining the origin with the…

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Q: Find the length of the arc of the curve x2 = (y − 2)3 from P(1, 3) to Q(8, 6).

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Q: Find the exact length of the curve. x = 9 cos(t) - cos(9t), y = 9 sin(t) - sin(9r), Ostsn 9 cos (47)…

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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: Compute 2z dz (2² – i)3 when y is any arc z = z(t) in C with |z(t)| > 2 for every t, with…

A: Let the required arc be ABC, which starts at z=3 and ends at z=2i: The shaded area shows a sector…

Q: Find the length of the arc from 0 = 0 to 0 = 2n for the cardioid r = f (0) = 2 – 2 cos 0.

A: Solution if r=fθ  has a continuous first derivativefor α≤θ≤β then length of polar…

Q: 6) Find the equation of the osculating plane of the helix x = sin 3t, y = 2t, at the point (-1,л,0).…

A: Given :x=sin3ty=2tz=cos3tpoint -1, π, 0

Q: 6. Find the arc length of the helix, r(t)=bcosti+bsintj+V1-b²tk from t= 0 to 27.

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Q: Find the length of the catenary y = a cosh from x = 0 and x = a X1.

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Q: Calculate Sc 2xyds, where C is the arc of x²+²=4 from the point (2,0) to the point (1,√3)

A: We know that ∫C f(x,y) ds=∫ab f( x(t), y(t) ) dxdt2+dydt2 dt

Q: Find the arclength on y = 4x3/2 from x is greater than or equal to 1 and less than or equal to 3

A: given: the function is y=4x32. we have to find the arc length on y=4x32 from x is greater than or…

Q: What is the area of one of the petals of the rose curve r = 2 cos(20)? T/4 cos (20) d0 8. cos (20)…

A: We have to find

Q: The arc length of the curve r= cos 30 with 0<0<T is J V (sin 30)² + (cos 30)² d0 T" V-9(sin 30)² +…

A:

Q: Find the arc length of the graph of x = 1 8y4 + 1 4y2 over the interval [1, 2].

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Q: what is the length of the curve y=1-cos(x) from x=0 to x=4pi

A: Given: y=1-cosx To find: We have to find the length of the given curve from x=0 to x=4π.

Q: The arc length of the curve r= cos 30 with 0<0 ST is I V-9(sin 30)² + (cos 30)² d0 0. I V(sin 30)² +…

A: