1. Consider the vector function (with values in R³) r(t) = ln (√2√1−t) i + (3 − √2√1 −t)j + 2 k Find a positive change of parameter from t to s where s is an arc length parameter of the curve having r(0) as its reference point.

Q: Let F(t) = (1, ²,4) and P = (2, 10, 4). Consider the curve C parametrized by F(t). Compute a tangent…

A: The objective of the question is to find the tangent vector, unit tangent vector, and the tangent…

Q: 3. Consider the following helix with vector equation 7 (t) = 2 cos (t) 7 (t) 7 + tỉ + 2 sin (a)…

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Q: Show that the graph of the vector-valued function r(t) = is a circle, and find its radius and…

A: The equation of a circle is defined by the equation, (x-h)2+(y-k)2+(z-l)2=r2 , where, (h,k,l) is the…

Q: Find r'(t)'r" (t) given the following vector function. r(t) = 3cos(t)i+ 4sin(t)j cost sint -25cost…

A: Given vector function is, r(t)=3cost i+4sint j

Q: Let 7(t) = (t + 4, – e*, 3 sin(3t)) - Find the unit tangent vector T (t) at the point t = :0 T(0) =

A: We have to find

Q: COS 1,sin 2t) and R(0) = (1,0.–1). Let R be a vector function such that T(t) = (cos 2t, 2/2, Find An…

A: Given : T→=32cos2t , 12 , 32sin2t, R→0=1 , 0 , -1. To Find: The equation of the osculating plane,…

Q: 5. Find the parametric equations of the line tangent to the curve C defined by the vector equation…

A: To find the parametric equation of the given tangent to the curve. The vector equation of the curve…

Q: Find the unit tangent vector to the curve given below at the specified point. r(t) = 7ti−2t²j¸ t = 4…

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Q: Sketch the curve with vector equation r(t) = (t2 – 2, t) in the xy-plane. Indicate with arrows the…

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Q: 2. Find thé moving trihedral of the curve C traced by the vector-valued function R(t) 4 cost i+4…

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Q: (A) Find A vector tangent and normal for the curve: x3 y = + 5 2 at the point (1, 5.5)

A: Note: Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Find a equation vector and the equation of the tangent line at the point P0 where t=0.2 on the graph…

A: The tangent is the line that just touches the curve at the point. The equation for the tangent line…

Q: Find r'(t), r(t), and r'(to) for the given value of to. r(t) = 3 cos(t)i + 3 sin(t)j, to r'(t) =…

A: The given vector valued function

Q: Find the unit tangent vector to the curve defined by =(- 4t, 4t, V49 - t) at t = - 6. T(- 6)

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Q: Let 7(t) = (3 cos(t), 3 sin(t), 3t) and P = (3, 0,6). Consider the curve c parametrized by F(t).…

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