Find an arc length parametrization r(t) = (e¹ sin(t), et cos(t), 7eª). Assume t(s) T1(s) = (0) = r₁(s) of 0 when s = 0, and t'(0) > 0.

Q: Find the following for the given equation. r(t) = (e-t, 5t², 7 tan(t)) (a) r(t) (b) r"(t) = (c) Find…

A: Given: rt = e-t, 5t2, 7 tan t To find: r't , r''t and r'(t)·r''t We know that  ddxex = ex ; ddxtanx…

Q: Find an arc length parametrization of r(t) = (e' sin(t), e cos(t), 2e*). r:(s) =

A: Calculate the derivative for r(t).

Q: Let C' be the circle |2| = 3 in positive sense. Find ( sin(r2*) + cos(72²) dz cos(T2²) (2 – 1)(2 +…

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Q: Find an arc length parametrization r, (s) of r(t) = (e' sin(t), et cos(t), 9et). Assume t(s)=0 when…

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Q: of dx- = 0, then dy |=0. Prove that is a function f is harmonic

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Q: Find the length L of the curve R(t) = e" cos(2t) i + e* sin(2t) j+2e"k over the interval [1, 4]. L =

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Q: Find the arc length of the curve c(t) = (5 cos(t), 5 sin(t), -13t) on the interval 0 ≤ t ≤ 2.…

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Q: Find the arc length of the curve c(t) = (cos(9t), sin(9t), 2t³/2) on the interval 0 ≤ t ≤ 1.…

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Q: 9) Find the arc length of r(t) = (cos 4t, sin 4t, t) from t = 0 to t = 2.

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Q: Find the length of the curve cos(t) + In(tan(;t)), y= sin(t), n/4 <t < 3T/4. x = %3D Length = %3D

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Q: d (h) Find sec (arctan (0~))] do

A: We need to find out the derivative.

Q: The curves F₁ (t) = (2 sin(t), 4 cos(t), e7t) and 72(t) = (3 ln(t), 4√t, t³) intersect at the point…

A: The angle between two curves is the angle between their tangents at the point of intersection .

Q: F(t) = 3 cos(t)ỉ + 3 sin(t)j + 2tk

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Q: Determine un ju should be a plane curve. ion f (0) so that x = a cose, y = a sin0, z = f (0)

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Q: If A = 100 0-2 0 004 Then A-1 =

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