Consider the helix r(t) = (cos(1t), sin(1t), 4t). Compute, at = 7:

Q: For the curve R (t) = (Sin2t, t, cosat) Find the unit tangent vector.

A:

Q: Find the Cartesian equation of r2 sin(20) = 1.

A:

Q: For r=sin40, (i) sketch the curve. (ii) Find the area of one loop of the curve.

A:

Q: Find the vector equation of the tangent line to F(t) = (2 sin 2t, cos 2t, – 6t) at the point where…

A: Consider the given vector. rt=2sint,cos2t,-6t   Find the derivative of the vector with respect to t.…

Q: Find f. f(t) f"(t) = 2e + 3 sin t, f(0) = 0, f(π) = 0

A:

Q: The curves T1 (t) = (3t, t°, – 4t°) and r2(t) = (sin(5t), sin( – 2t), t) intersect at the origin.…

A: We have to find the direction vector first.

Q: 1) Let 7(t) = (t, 2 cos t, 2 sin t), -4 <t< 4. Find the length of the curve.

A: In

Q: A glider is soaring upward along the helix r(t) = (cos t)i + (sin t)j + tk. How long is the glider’s…

A: Given: The path of glider as r→t=cost i^+sint j^+t k^, To find: The length of the glider's path from…

Q: 11. Find T(t), N(t), B(t) and x(t) for the circular helix: r(t) = (sin5t,- cos5t,12t)

A:

Q: Find the length of the curve r(t) = (5 cos(2t), 5 sin(2t), 2t) for − 2 ≤ t ≤ Give your answer to two…

A:

Q: curve R(t) Find the parametric equations of the tangent line to the (2t, cos 2t, sin 2t) at the…

A: What is Tangent Line: The straight line that only touches the curve at a particular location is…

Q: Let r(t)=(10 cos(t), 1, 10 sin(t)). Find the unit tangent vector u drawn to point P=(6,1,8). Sketch…

A:

Q: Find T, Ñ and B for the curve r(t) = = (3 cos (5t), 3 sin(5t), 2t) at the point t = : 0 Give your…

A: