3. The principal normal vector field is defined by : T'(s) (c)\T' (s) T'(s) (a) T¹ (s)\ r'(t) |r' (t) If r(t) = (cos3t, sin3t, 0), the length of r is: (b)

Q: Find the derivative of the vector function r(t) = ln(19 - t²)i + √17+tj − 7e-¹t k - r' (t) = (¯¯

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Q: Let r(t) = (e", e", te") be a vector function. Find; 21 -2t (a) r'(1) (b) r"(1) %3D

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Q: 3. The principal normal vector field is defined by : r' (t) (a) \T' (s)\ (b) (c) |T'(s) | [r' (t)]…

A: Given : rt=cos3t,sin3t,0 To find : Length of r and  principal normal vector field .

Q: 5.- Determine the tangential and normal components of the acceleration for the vector function:…

A: Step 1:Step 2:

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A: First we will plot the given parameters.

Q: Suppose r'(t) has units of m/s. Explain why T(t) = r'(t)/ | r'(t) | is dimensionless (has no units)…

A: Suppose r'(t) has units of m/s. To explain why Let r(t) be a differential vector valued functionNow…

Q: Find the derivative of the vector function r' (t) = ( -> r(t) = ln(5t²)i + √√19+tj-8e²t k ID 9 9

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Q: For each of the following sequences, if the divergence test applies, either state that lim an does…

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Q: r(t) = (4+t)i+(9+ln(cos t))k, -pi/2 < t < pi/2 Find principal unit  normal vector N for the curve…

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Q: Find the derivative of the vector function r(t) = In(10 – t) i+ v10+tj+ 8e-8* k r'(t) = (

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Q: Find a tangent vector of the curve7(t) = (t², 2 sin(t), 2 cos(t)) at (0,0, 2) (0,0,1) (1,0,0) None…

A: Here, Find it’s derivative This is the tangent at any point on the curve.