Given r(t) = <2 cos(t), 2 sin(t), 2t>. • What is the arc length of r(t)...

Given r(t) = <2 cos(t), 2 sin(t), 2t>. • What is the arc length of r(t) from t = 0 to t = 5. SET UP integral but DO NOT evaluate • What is the curvature κ(t)?

Expert Solution

We setup an definite integral that represent the Arc length of the given curve.

We find out the curvature of the given curve by using curvature formula.

milcah answered 2 years ago

Consider the helix r(t)=(cos(2t),sin(2t),−3t)r(t)=(cos(2t),sin(2t),−3t). Compute, at t=π/6 A. The unit tangent vector T=T= ( , ,...

Consider the helix r(t)=(cos(2t),sin(2t),−3t)r(t)=(cos(2t),sin(2t),−3t). Compute, at t=π/6 A. The unit tangent vector T=T= ( , , ) B. The unit normal vector N=N= ( , , ) C. The unit binormal vector B=B= ( , , ) D. The curvature κ=κ=

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y''+y=2t+1+(cos(t))^-2

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If u(t) = < sin(5t), cos(5t), t > and v(t) = < t, cos(5t), sin(5t) >,...

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Let r : R->R3 be a path with constant speed, satisfying r"(t) = (4 sin(2t))i +...

Let r : R->R3 be a path with constant speed, satisfying r"(t) = (4 sin(2t))i + (-4 cos t)j + (4 cos(2t))k for all t belongs to R: Find the curvature w.r.t. t of r. (Hint: cos(2t), sin(2t), and cos(t) are linearly independent. i.e. if c1cos(2t) + c2sin(2t)+ c3cos(t) = 0 for all t belongs to R, then c1 = c2 = c3 = 0.)

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