Consider the spiral curves given parametrically by x(t) sin t tr where r > 0. 5.a Using that x' (t) = y(t) = t cost r sin t cos t tr and y' (t) " = t> 3 t sint + r cos t tr+1 tr+1 set up and simplify an (improper) integral that computes the arclength of these spirals. The integral will depend on r. 5.b For which r > 0 does this spiral have finite length? 5.c Compute the length of the spiral when r = 3.

Q: Find the arc length for the parametric x = e' cost; y = e' sin t; 0sts2n and sketch it curve below.

A:

Q: Find the arc length of the curve r(t) = (4t^2, 2(sqrt4)t, ln t), for the domain of t between 1 and…

A: We have to find Arc length.

Q: 4³/² on 2 ≤ x ≤ 4.

A:

Q: Find the curvature of the given curve y(x) = In(secx) a. 1/(Sec?x + 1) b. Cosx//1+ Cos²x C. Secx d.…

A:

Q: Find the exact arc length of the curve y =2V on the interval [0,11]. 70 +60 +50 +40 +30 +20

A: The objective of the question is determine the arc length of the given curve.

Q: Find the moving trihedral of the curve R(t) = (e^t)sin(t)i − (e^t)cos(t)j + (e^t)k at any t in the…

A:

Q: Find the arc length of the indicated portion of the curve given by r(t)= 2r°i+11r'j+10r'k, -1<t52

A: Solve the following

Q: Find arc length of r = 1/0 on (1, 2nt)

A:

Q: Find the Arc length of  y= 1+x^1.5 on  [0, 1]

A:

Q: Find the arc length parameter along the curve from point where t=0 r(t)=(e^t cos t)i+(e^t sin…

A:

Q: For the curve r-y +2xy-y+1=0: a) Find the derivative dy/dx. b) Where do the horizontal tangent lines…

A: follow the next step

Q: Find the arc length parameter along the curve from the point where t = 0 by evaluating lo (1)| dr S…

A:

Q: Use parametric-form integration to find the Arc Length of the arc x=(1/3)t^3 defined by y=(1/2)t^2…

A:

Q: Consider the section of curve y=12x2 from (2,2) to (4,8). None of the following need to be…

A: solution is given below..

Q: To identify how much heat is required to bring a kettle of water to its boiling point, you are…

A: Here,