a The curvature of the helix r(t) = (a cos t) i + (a sin t) j+ bt k (a.b2 0) is K= What is the largest value K can have for a given value of b? %3! a? +b?

Q: Find the moving trihedral and the curvature at any point of R(t) = (t²,– cos 8t, sin 8t).

A: Moving trihedral are three unit vectors of curve  Unit tangent vector  Unit normal vector  binomial…

Q: Q2/Find the curvature of the curve, r= (4 cos n i+4 sin n j)

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Q: a The curvature of the helix r(t) = (a cos t) i + (a sin t) j + bt k (a,bz 0) is K=- What is the…

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Q: 4. Find the curvature * 5 K of the curve ř (1) = (e' cos(t), e' sin(t), 3) at t = 0.

A: Given data: The given expression for the curve is r→(t)=et cost, et sint,3. The given point is t=0.…

Q: * Find the curvature .12 (ähä 2) K of the curve ř (t) = (e' cos(t), e' sin(t), 3) at t = 0. %3D

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Q: 32. At what points does the helix r(t) = (sin t, cos t, t) intersect the sphere x? + y² + z² = 5?

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Q: Find the radius of curvature of the curve y = √√x at x = 1 5√5 2 5√5 b) Sys c) 5√5 d) none 2 a) ind…

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Q: Find the curvature and the radius of curvature at the point t = 0. x = e' cos(t), y = e' sin(t), z =…

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Q: Find the radius of curvature at origin at (0,0) y - x = x2 + 2xy + y2

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Q: Show that the volume of solid formed by revolving one loop of the curve r2 = a? cos20 about the line…

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Q: Find the extreme values of the function z= &r+2ry-3r+y+1 and show that only one of the two extrema…

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

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: Find the curvature K, where s is the arc length parameter. 5s i+5sin /706 5s 6. sk V706 r(s) =5 cos…

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Q: 3. Find the radius of curvature at any point of the curve y = a Cosh ( x/a)

A: solution:-  The given curve is  .y=a coshxa.........eqo1

Q: Find the curvature K of the curve at the point P. r(t) = Pi + tj + 1, 3 2 K = %3D

A: Given that rt=12t2i+tj+13t3k and point is P12,1,13. It is required to find the curvature K at the…

Q: 2, The hadiusS r of a sphere is increasing as a vate af 3amimin. Find the rate af Ghane e Of Ahe…

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Q: 3) Find the radius of curvature for the parametric X = сurve e-t cos t , y = e=t sin t.

A: R=1+dydx232d2ydx2 Given equations of curve- xt=e-tcostyt=e-tsint

Q: 1. Find the moving trihedral and the curvature at any point of the curve R(t) = cost î + sint j+k.

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Q: the detined b is Constant. Curiature a(t) =| 1 Cost, 1 sint, o of the curve d:laa)tR? where Find

A: We are given : α(t)=1rcos t,1rsin t,0 ⇒α'(t)=-1rsin t,1rcos t,0 Now, the Unit tangent Vector is :…

Q: Find the radius of curvature of the curve r = at 0 = 1+cos 0 O 5.9665 O 5.6965 O 5.6569 5.5966

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Q: Find the curvature of the curve r (t) (2 cos(5t), 2 sin(5t), 4t) at the point t = 0 CoS Give your…

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Q: The curvature of a point moving along the curve given as R(t)=(In sec t) i+ tj is: O t O sec t O…

A: Here, Rt=lnsecti+tj

Q: Find the curvature and the radius of curvature at the point t = 0. x = e' cos(t), y = e' sin(t), z =…

A: We have to find the curvature and the radius of curvature at the point t = 0. x = et cos(t)  ,…

Q: 1) Find a curve a = 7(s) in are length s with torsion 7= 0, and curvature k(s) m = constant. %3D 8+…

A: Consider the provided question, Torsion τ≡0,curvature ks=1s+mRadius of curvaturer=kk2+τ2…

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: 3) Find the radius of curvature for the parametric сurve e-t cos t y = e-t sin t.

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Q: Find the length of the spiral r = eθ/√2 from θ = 0 to θ = π.

A: Given Differentiating r with respect to thita ,we get

Q: Consider the curve r = (cos t, sin t, t). If u is the unit tangent, n is the unit normal and k is…

A: Given :             r(t) = cos t , sin t , t      Calculate the derivative :…

Q: 4. Given YZ tangent to oJ at point Y and m<WYZ = 104, %3D what is the measure of WXY?

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Q: 4. Find the length of the arc C = {(x, y): y = V16 – x²?,0 < x < 3}.

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Q: Find the speed of the cycloid c(t) = (4t − 4 sin t, 4 − 4 cost) atpoints where the tangent line is…

A: Given: c(t)=4t-4sin(t), 4-4cos(t)

Q: Find the curvature of the curver(t) = (4 cos(t), 4 sin(t), 5t) at the point t = 0 %3D Give your…

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Q: The curvature of the curve 7 (t)={2t, 2t+1, sin2t) at t= is 4 O 1 O 1 O 2 1/818 1/2

A: Here the given curve is r(t)⇀ ==(2t,2t+1,sin2t) Here we have to find the curvature of the curve at…

Q: The curvature of the curve 7(t)=6t, 6t+1, sin2t) at t= is 4 18 1 8 0 1 1/2 2.

A: we have to find the curvature

Q: The curvature of the curve 7 (t)= (2t, 2t+ 1, sin2t) at t= TT is 4. 1 18 O 1 1/8 1/2 O O O O

A: The given curve is r(t)→=2t,2t+1,sin(2t) We know that the curvature κ(t) for r(t)→ is given by the…

Q: Find the exact value of arc length of the semicubical parabola y2 = x³ between the points (1,1) and…

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Q: 6. Consider the same curve from the last problem, C parametrized by T(t) = (2 cos t, –1,2 sin t)…

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Q: Find the curvature of the curve r(t) = (cos(t), sin(t), 3t) at the point t Give your answer to two…

A: Curvature is a measure of how much the curve deviates from a straight line. The formula for the…

Q: Consider the curve -(cos t, sin t, t). If u is the unit tangent, n is the unit normal and K is the…

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Q: 2. The Cornu (or Euler) spiral, shown below, is defined by r(s) = (f* cos (u²) du, f *cos (u²) du,…

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Q: Find the curvature K of the curve, where s is the arc length parameter. M03 - (1+²)+(1-2) r(s) K =

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Q: s) Evaluate the line itegral ( +2y + 2)dy – dz, where C is the arc of parabola z = 2+ y". from (2,0)…

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Q: Find the curvature K of the curve, where s is the arc length parameter. V2 r(s) : K =

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Q: 6. Find the radius of curvature of the cycloid x= a( t-sin t), y = al 1-cos t).

A: 6. The parametric equation of the given cycloid is x=at-sint, y=a1-cost. First, evaluate the first…

Q: Find the moving trihedral and the curvature at any point of R(t) = (t²,– cos 8t, sin 8t). -

A: Given is : R→(t)=t2,-cos(8t),sin(8t) In order to find the curvature use the formula . Formula for…

Q: i the the position vecor be R(t) = CoS s(2t),e¯tsin(2t) ,0). Compute the curvature k(t). e

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Q: Find an arc length parametrization of the line y = 8x + 7. r;(s) II

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Q: 10. Find the curvature K of the given curve. r(1) = ti +2sin(t)j+2cos (1)k

A: Curvature κ of the given curve r→(t) is T→'(t)r→'(t) where T→(t) = r→'(t)r→'(t).

Q: Find the curvature of the curve 7(t) = (3 cos(4t), 3 sin(4t), 4t) at the point t %3D Give your…

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