Find the unit tangent vector T(t). r(t) = t'i + tj + k, P(16, 4, 16/3) T(4) = Find a set of parametric equations for the line tangent to the space curve at point P. (Enter your answers as a comma-separated list. Use t for the variable of parameterization.)

Q: Let R(t) = (t²,1 − t², t) and r(t) = cost. Determine the parametric equations of the line tangent to…

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Q: The equation of the tangent plane to this ellipsoid at (1, –2, –2) is The vector parametric form of…

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Q: 0I. Also, r(t) = (2cos t)i + (2sin t)j + (/5t)k, 0stsn Find the curve's unit tangent vector. T(t) =…

A: Differentiate and take magnitude and use it for unit tangent vector

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

A: The given curve is rt=t2+1,4t12,et2-t. Notice that the given curve satisfies t=1(If t=1 is plugged…

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A: The line integral ∫CPdx+Qdy+Rdz involves integration over a specific path. The general form of the…

Q: Consider the smooth parametric curve 6 defined by the equations t (t²-3) { 3 (t²- 3)' = = where t€…

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Q: find the unit tangent vector T(t) and find a set of parametric equations for the line tangent to the…

A: Solve the following

Q: Find the equation of the line tangent to the parametric curve (pictured below) defined by I=, y=t+t…

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Q: 3. Let R(t) = (t²,1 - t², t) and r(t) = cost. Determine the parametric equations of the line tangent…

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Q: Find the unit tangent vector to the curve defined by 7(t) = (4 cos(t), 4 sin(t), 5 sin°(t)) %3D 37…

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Q: Consider the curve C given in parametric equations as t(t – 1)2 In (4t² + 1) %3D C : for t e R. (a)…

A: Given problem is :

Q: 2. Find the parametric equations of the tangent line to the curve as result of the intersection of…

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Q: 3. Let f(x, y) = xy+ y². Find the equation of the tangent line in parametric form in the x-direction…

A: Solve the following

Q: Let C be the curve with parametrization r(t) = cos(t)i + sin(t)j – 2tk. a) Find the parametric…

A: Let C be the curve with parametrization   rt=costi+sintj-2tk We have to find parametric equations of…

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Q: Sketch the graph of 7(t) = sin(t)i – 2cos(t)j–tk in 3-space; then find and draw the tangent vector…

A: Given, r→t=sinti^-2costj^-tk^

Q: 2. Consider the function 7(t) = (t² - 4,t – 2,v80 + 4t + 7t? - t*). Find parametric equation(s) for…

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Q: Find the unit tangent vector T(t) and find a set of parametric equations for the line tangent to the…

A: Given the curve     rt=2sin(t),2cos(t),4sin2(t) and the point P1,3,1.

Q: A curve is defined as the parametric equations: 1 x = acose, y=-asin 0, 0<0< 2n dy where a is a…

A: on solving this we get

Q: Find a rectangular equation for the plane curve defined by the parametric equations. x = t + 4, y =…

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Q: 16. Sketch the parametric curve x = Vt, y= sin t, 0<t< 2n. (b) (a) 1.0 (c) 101 1.0 0.5 0.5 0.5 05 10…

A: The graph of the parametric curve x=√t, y=sint , 0≤t≤2π is given as below,

Q: Let w = 8y dx + 8x dy + dz be a one-form on R3. Find a parametric curve a : 0, 1] → R³ such that W =…

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Q: Find the parametric equations of the tangent line LT to the curve C:r (t) = 2 cos(t)i + sin(t)j +…

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Q: Find the length of the parametric curve C = {(x(t),y(t)) : t E I} x(t) = cos (t) , y(t) = sin³ (t),…

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Q: Let r(t) = be a vector function. a. Find the tangent vector r'(1) when t = 2. b. Find the…

A: To find tangent vector , parametric equation of the tangent line to the curve , the arc length.

Q: Find the unit tangent vector T(t), and find a set of parametric equations for the line tangent to…

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Q: Let R(t) = (²,1-t², t) and r(t): = cost. Determine the parametric equations of the line tangent to…

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Q: 4 1. r(t)=t²i+t j+ k 3 4 1,1, 3 at -

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

Q: Find the unit tangent vector to the curve defined by 7(t) = (4cos(t), 4sin(t), 3 sin (t)) at t = 4…

A: “Since you have asked multiple questions in a single request, we will be answering only the 1st…

Q: Find the parametric equations of the tangent line LT to the curve C:r(t) = 2 cos(t)i + sin(t)j+ 2tk…

A: A parametric equation of a curve is given by: C: r(t) = 2cos(t)i + sin(t)j + 2tk Now, we have to…

Q: 4. Find the parametric equation of the tangent line to r(t) = 4costi – 3tj %3D at Po(2, –n)

A: Given: To find the parametric equation of the given tangent line as follows, r(t) = 4 costi- 3tj…

Q: Find a vector parametrization of the curve z = :-222 in the xz-plane. Use t as the parameter in your…

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Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

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Q: 6. Find a set of parametric equations for the line tangent to the space curve at the given point. 2…

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Q: Find the length of the parametric curve x = e^t + e^-t, y = 5-2t on the interval [0,3]

A: Find the length of the parametric curve x = e^t + e^-t, y = 5-2t on the interval [0,3].

Q: r(4)=DTsin(i+ 34 j+ t°K 2. POINT: (1,2,1)

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Q: Find a parametric description for the curve y=4-x^2 from (-2, 0) to (2, 0) such that t=0 corresponds…

A: Given: The curve y=4-x2 from (-2,0) to (2,0)

Q: Find the unit tangent vector to the curve defined by 7(t) = (2 cos (t), 2 sin(t), 4.sin (t)) at t =…

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Q: Consider the curve r(t) = (t, 3 cos t, 3 sin t) for t 2 0. Find an equation for the projection of…

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Q: Find the unit tangent vector r(t) = t2i + tj + 4/3k and a set o f parametric equations P(1, 1, 4/3)…

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Q: 2. Consider the function 7(t) = (t² - 4, t – 2, v80 + 4t + 7t² - t*). imothy e startin Find…

A: Given, x= t²-4 y= t-2 z= √(80+4t+7t²-t⁴) (xp,yp,zp)= (-3,-1,√90)

Q: Find the unit tangent vector T(t). r(t) = ti + tj+ k, P(4, 2, 8/3) T(2) = Find a set of parametric…

A: To determine: (1) The unit tangent vector . (2) The parametric equations for the line tangent to the…

Q: 4. Let r(t) = 2 sin(t) i+ 2cos(t) j+4 sin?(t)k Find a tangent vector at the point P = 7=) = (1, v3,…

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Q: Find the length of the parametric curve C {(x(t), y(t)) : t E 1} x(t) 4cos(t), y(t) = 4sin(t), with…

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Q: A curve is defined by the parametric equations z (t) = at and y (t) = bt, where a and b are…

A: Given,  We have  xt = at   and yt = bt  ;  where a and b are constants.  We have to find the length…

Q: Find parametric equations for the tangent line to the curve with the given parametric equations at…

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Q: 2. Find parametric equations for the tangent line to the curve r(t) = (t8,t³,t7) at (1,1,1).

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Q: 38. Let r(t) = (1³ -1- 2)i + 4r* j. %3D (b) Find parametric equations for the tangent line to the…

A: Topic = Vector

Q: ) Find the equation of the tangent line (in terms of x and y) to the parametric curve at the given…

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