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Find the length of the curve with the given vector equation. r(t) = (1 + 4t)i + (1 + 3t)j + (2 – 2t)k, -1 ≤ t ≤ 0 Type your answer in the given answer box.  You may need to use the equation editor found in the editing menu.  If the equation editor is not showing, click on the three vertical dots to expand the menu.  

Find the length of the curve with the given vector equation. r(t) = (1 + 5t)i + (1 + 6t)j + (3 – 3t)k, -1 ≤ t ≤ 0 Type your answer in the given answer box.  You may need to use the equation editor found in the editing menu.  If the equation editor is not showing, click on the three vertical dots to expand the menu.  

Find the indicated derivative for the given vector-valued function .Find r ‘ (t) for r(t) = (t4)i – (csc t)j + 4k.

Find the indicated derivative for the given vector-valued function .Find r ‘ (t) for r(t) = (t6)i – (csc t)j + 10k.

Find the length of the curve with the given vector equation.r(t) = 4ti + j + k; -6≤ t ≤ 1

Find the curvature of the curve r(t).r(t) = (5 + 5 cos 10t) i – (7 + 5 sin 10t)j + 3k

The position vector of a particle is r(t). Find the requested vector.The velocity at t = for r(t) = 5sec2(t)i – 9tan(t)j + 6t2k

Compute r”(t).r(t) = (3 ln(6t))i + (9t3)j

If r(t) is the position vector of a particle in the plane at time t, find the indicated vector.Find the acceleration vector.r(t) = (8 ln(3t))i + (2t3)j

The position vector of a particle is r(t). Find the requested vector.The velocity at t = for r(t) = 4sec2(t)i – 5tan(t)j + 7t2k