For the following exercises, find the arc length of the curve on the indicated interval of the parameter. 114.Find the length of one arch of the cycloid x= - - 4(t- sint), y= 4(1– cost).

Q: Find T,N and k for the curve:

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Q: Determine the arc lenght of the curve 9x2 = 4(y² – 1)³for 1 <y<2.

A: This question is related to calculus.

Q: H.W. 1. Find the arc length of the curve x = (y + 2)2 from y-0 to y-1

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Q: (b) (i) Parametrise the graph of the C function y = f(x), for x = [a, b], as the track of a regular…

A: b) (i) Hint: A mathematical process known as parameterization involves representing the state of a…

Q: Determine the 2nd derivative. x^2 + 4xy + y^2 = 2

A: Given equation x2+4xy+y2=2

Q: Find the radius of the osculating circle to the curve r(t) = (cost,3sint) IT at t = 3

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Q: r(t)=(cost+t sint)i+(sint -t cost)j, a/2<15a. %3D

A: We have to find arc length of given function.

Q: Compute the arclength of the following curves. (y-1)³ =x², for 0 <x< 5 а.

A: We have to compute the arc length for the function y-13=x2, for 0≤x≤5.

Q: Find the unit tangent = (a cos t, a sin t, b t) - at any point. Also find the length of one to the…

A: r=acost, bsint, bt, -∞&lt;t&lt;∞ where a&gt;0

Q: Find the length of the curve: r = 4cos³(0/3),0 < 0 < ? 2

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Q: Find the path of the sloping path y = x² + c such that θ = π / 4 is the angle between the tangents…

A: Slope = 1  Point are (a,b) So equation of tangent      Y-b = 1.(x-a)

Q: Find the length of the curve a = 3y from y = 0 to y = 5. Round your answer to four decimal places.

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Q: Set up and simplify (but do not evaluate)/ F. dr, where F(x,y) (x2, xy), andC is the arc of the…

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Q: What are the coordinates of the point on the curve f(x)=x- 4 where the tangent is horizontal?

A: To find the co-ordinates of the point ..

Q: (у — сos*x)dx + cos x dy %3D 0

A: We need to find the solution of y-cos2xdx+cos x dy=0 This differential equation can be written as:…