Given the vector-valued function R(t) = -6cos(1-2t) i+8t j+6 sin(1 2t) k. Find: (a) the length of arc of the curve from t = In 2 to t= In 4; %3D (b) the unit tangent vector at t (c) the unit normal vector at t %3D

Q: Find the unit tangent vector to the curve defined by F(t) = (4 cos(t), 4 sin(t), 3 sin²(t)) at t = 3…

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A: Given :                   r1(t) = cos t , sin tr2(t) = sin t , cos t

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A: Note: Since we can solve at most one problem at a time, we have solved the first one. Kindly…

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Q: The curves 71(t) = (- 5t, t°, 3t*) and r2(t) = (sin(5t), sin(2t), t) intersect at the origin. Find…

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Q: a:1 c R E4 t a(t) = (cos (), sin (), 2, at) %3D ↑

A: Given the curve  α:I⊂ℝ→ℝ4 given by t→αt=cost2, sint2, 2, αt

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Q: graphically represent the curve described by the following functions f (t) = (sin t, 2cos t)

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A: We have to find the unit tangent vector at t=pi/3

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A: Given position vector is R→t = cos3t i +sin3t j +3t k Function fx, y, z =x y z

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A: To find all parameter of given graph we need to first find Vm then use time period to find angular…

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Q: In which direction is the curve x = -2 sin t, y = 2 cos t, for 0 ≤ t < 2π, generated?

A: x = -2 sin t, y = 2 cos t Table for values of x and y: t x y 0 0 2 π 0 -2 π2 2 0 2π 0 2

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A: For horizontal tangent, equate slope of tangent = 0 Slope of tangent = f'(x)

Q: Find the equation of the tangent line on 3xe™v² - ez 2ye at (1,1)

A: Given  3xexy2-ex3=2yex2first we find dydx at point (1,1)