2. Consider the function 7(t) = (t² - 4, t – 2, v80 + 4t + 7t² - t*). imothy e startin Find parametric equation(s) for the tangent vector to the curve at the point (-3, –1, V90). rom lo ve alrea ment for

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: Let r(t) = (-5t5 - 3, 4e-4t, 5 sin(2t)) - Find the unit tangent vector T (t) at the point t = 0.…

A: Given vector  r(t)→=<-5t5-3,4e-4t,-5sin(2t)>

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A: We have given equation of tangent plane 2x+2y=9which is incorrect because left side is even number…

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Q: Let C be the parametric curve defined by (x(t) = t2 – t – 2, 1 y(t) = t³ – t² + t. Determine if C is…

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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 =9…

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

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Q: 1. If the parametric curve $x=f(t), y=g(t)$ satisfies $g^{\prime}(1)=0,$ then it has a horizontal…

A: TRUE Slope of the curve, when in parametric form = dy/dx = g'(t) / f'(t)

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 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: use the given graphs of x = ƒ(t) and y = g(t) to sketch the corresponding parametric curve in the…

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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 :

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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: In Exercises 31-36, find a parametrization of the tangent line at the point indicated. 31. r(t) =…

A: The parameterization of the tangent line is given as L(t)=r(t)+t r'(t)

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 parametric curve r = t + 1, y = t - t. dy (a) Find d.r dy (b) Find da?

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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: Consider the curve C parametrized byx = (t^2+1)/(t^2-1) and y = (2t)/(t^2-1) for all t in (−∞, −1 )…

A: Given:

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A: Find slope and then use equation of tangent line

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A: Given that rt=3cost,3sint,9 P32,32.9 To find the parametric equation for the line tangent to the…

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: 1. Find the tangent vector to the curve 6t r(t) = [t3 – t, (2t + 1)*] t+1 at t = 1.

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Q: x(t) = t², y(t) = t³ – 3t, on – ∞ <t < ∞ %3D а. Show that the parametric curve has two tangent lines…

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Q: Let C be the parametric curve defined by Sx(t) = t2 – t – 2, |v(t) = t* – º +t. Determine if C is…

A: Substitute x=-2 in the given equation xt=t2-t-2 and simplify to calculate the value of t.…

Q: use the given graphs of x = ƒ(t) and y = g(t) to sketch the corresponding parametric curve in 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: Consider the parametric curve defined by 1 a(t) %3D y(t) = t² || What is the slope of the line…

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Q: Consider the smooth parametric curve defined by the equations = t (t²-3) { = 3 (t²-3) ¹ where t € R.…

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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: Find for the parametric curve c(t) = (41°, 2r² – 8) at the point t = 2. (Use symbolic notation and…

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Q: Find the work done by F = xyi+yj - yzk over the curve r(t) = ti + t²j + tk, 0≤t≤1

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Q: Let l be the line y = - (7x + 5) in R21 Find vectors dland b so that v = a + tblis a parametric…

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Q: 2. Find the work done by F in moving a particle once counterclockwise around the given curve C F =…

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Q: -2 Find the projection of v = 1 onto the line l of R³ given by the parametric equation l = tủ, where…

A: We will find out the required projection.

Q: Find the length of the curve defined by the parametric equations y = 4 In((t/2)² – 1) from t = 9 to…

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Q: Find the length of parametrized curve given by x(t)=−6t^2−6t,y(t)=−4t^3−6t^2 where t goes from 0…

A: Given information:  The parametric equations are x(t)=−6t2−6t,y(t)=−4t3−6t2 over the interval .0≤t≤1…

Q: Consider the following parametric curve: x(t) = 3t^2 −6 and y(t) = 3t^4 −3t^2 +12t +10 Find the…

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Q: Determine the torsion at t = 0 of a curve a : [−1, 1] → R3, a(t) = (2t, t^2, t^3/3). Moreover,

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Q: Please help solve this. If this can be solved without linear algebra I would prefer to see that…

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Q: Which is the graph of the derivative dyldx of the parametric equations x(t)= 3cos t and y(t)=3sin t…

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Q: Let 7(t) Find a parametric equation of the line tangent to 7(t) at t = 1. In particular,…

A: To find: The parametric equation of the tangent of the line tangent to r→t. Given: The parametric…

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A: Solution is given below:

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: 1. Let C be the parametric curve defined by Determine if C is concave up or concave down at…

A: Given parametric curve isx(t)=t2-t-2,y(t)=t3-12t2+tThe concavity of the curve C at the point -2, 32…

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Q: Find the natural parametrization of r(t) = 1²0₂ + 20y. What is this curve?

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