Sketch the graph of the following parametric (a) x = 1+t , y= 2t – 3, 2

Q: Find the slope of the tangent line to the parametric equations: x = 3t2 - 3, y = 2t + 1 at t = 1. %D…

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Q: I. Let C be the parametric curve with parametric equations x=t(t² + 1)-¹/2 te [-3,3] ly: = 2t - 2…

A: There are two points at where the tangent line is horizontal

Q: 7. Find the length along the parametric curve defined by v(t) = (t, In(cos(t))) from t = 0 andt=.…

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Q: Find parametric equations of the tangent line to the curve of intersection of paraboloid z = x² + y²…

A: We know that tangent line to ellipse will be perpendicular to normal of both the surface. Therefore,…

Q: (a) Sketch the graph of the parametric curve. x = 3 sin t + 3 y = 2 cos t (0 s tsn)

A: a) The given parametric curves are, x=3sint+3y=2cost The equations can be written as,…

Q: Express the parametric curve in the form y = f (x). x = tan t, y = sec t

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Q: 27. Show that the curve with parametric equations x = t cos t, y =t sin t, z = t lies on the cone z²…

A: To Show: i. Show that the curve with the parametric equationx=tcost, y=tsint, z=t  lies on the…

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 parametric equations for the tangent line at the point (cos(−4π/6),sin(−4π/6),−4π/6) on the…

A: Given parametric equation of given curve is x=cos(t), t=sin(t), z=t Differentiate with respect to t.…

Q: Find the slope of the tangent to the parametric curve c(t) = (cos t, sin t) at the point (–1/2,…

A: We need to find the slope of the tangent to the parametric curve c(t)=(cos t, sin t ) at the point…

Q: The unit circle x² + y=1 can be wrriten in parametric form as x = cos(0) and y : = sino. dy and…

A: Follow the procedure given below

Q: Determine the area under the parametric curve defined by the equations x-t2-4 and y=t on the…

A: To find: The area under the parametric curve x=t2-4 and y=t on the interval 0,3. Formula used: The…

Q: Find the tangent line equation to the parametric curve x = cos t y = sin³ t at t = V2 O A. y = -x +…

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

A: Parametric equations for a line:

Q: Consider the curve given by the parametric equations x = sin t, y = sin(t + sint) where -oo <t < ∞.…

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Q: Graph the curve with parametric equations x = sin(t), y = 3 sin(2t), z = sin(3t). H0.0 y -0.5 0.5…

A: The graph will look like this:

Q: 7. Find the slope of the tangent to the parametric curve x = t - lnt, y = t + lnt at the point (e +…

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Q: Use the arc-length formula of the parametric equation and evaluate the arc-length of the curve while…

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Q: Let 3 x = cos' t, y = sin³ t, z = 7; 0 < t < r. Find the arc length of the parametric curve.

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

A: The given parametric equation is: x=5 ln t  ,   y=4t   ,      z=t3 Given point is:  (0, 4, 1) From…

Q: Find the exact value of x²y³z ds, where C is the curve with parametric equations x = e-t cos(5t), y…

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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: Sketch the regions enclosed by the given curves. y = 2 cos(5x), y 2 sin(10x), x = 0, x = 1/10 2.0…

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Q: a) Compute the enclosed area and length (from 0 to 2pi) of the parametric curve given by 3, 3, x = A…

A: Note: Hi! Thank you for the question as per the honor code, we’ll answer the first question since…

Q: 1. Consider a fence whose base is the path with parametric equations |x(t) = cos³ t, |y(t) = sin³t,…

A: Given, A fence whose base is the path with parametric equations xt=cos3tyt=sin3t for 0≤t≤π2. Let the…

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: 1. Eliminate the parameter to find a Cartesian equation of the curve given parametrically by (x(t),…

A: Recall: sin2t+cos2t=1

Q: A parametric curve is defined by : I) x = 5sin(t ) – 2; y = 1– 3 cos(t ) ; 0sisa

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

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: B. Find the length of the circle of radius r defined parametrically by x = r(v1 – sin t) and y =…

A: We need to find the length of the circle which is parametrically defined as below.

Q: Consider the parametric curve given by (a) Find dy/dx and d²y/dx² in terms of t. dy/dx d²y/dx² = = x…

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Q: Find parametric equations of the line tangent to the graph r(t) = (t cos 7t)i - (t+ t)j+ sin(t)k at…

A: Given that rt=t+cos 7ti-t2+tj+sintk   Tangents to the curve is given by Tt=ddtrt Tt=ddtt+cos…

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: Suppose a curve is traced by the parametric equations 3(sin(t) + cos(t)) = x у 3 18 — 6 соs"(€) — 12…

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Q: Find a parametric description for the curve x=y^2-9 from (0, 3) to (-5, -2) such that t=0…

A: We need to parametrize the curve x=y2-9 from 0,3 to -5,2 We need to put either x=t or y=t and see a…

Q: Find an equation y = f(x) for the parametric curve c(0) = (cos(0), 3 cos(0) + 8 sin²(0)) and compute…

A: The objective is to find y(x) and it's it's derivative .

Q: Find an equation of the tangent(s) to the curve with parametric equations x = 1+ vt, y = e at the…

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Q: ..... The area of the surface generated by revolving the curve x = 1 cos (2t), y = 7+ -sin (2t) on…

A: Follow 2nd and 3rd step.

Q: Determine the concavity of the parametric curve when t = 2 where x = 1+ t², y = t-t³ Compute the…

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Q: Sketch the regions enclosed by the given curves y-4 cos(7x), y- 4 sin(14x), x -D, x-/14 0.05 0.10…

A: The solution of above question is written below.

Q: If y = x2 is expressed with parametric equations such that = 6 when x = 1, what is ? dt dx %3D dt

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Q: Consider the parametric equations x = a cos3 t and y = a sin3 t with 0 ≤ t ≤ π. Find the surface…

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

A: Answer

Q: Let curve C be the arc of x2 + y2 = 16 traversed once counterclockwise from (0, 4) to (0, -4). Let…

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Q: 1. Sketch the parametric curve x = (cos t) (1+ cos t), y= (sin t) (1 + cos t) , 0 < t < 27 .

A: we have been given the parametric curve x=(cos t)(1+cos t) and y=(sin t)(1+cos t) where 0≤t≤2π

Q: r(t) = (e-t cos t, e-t sin t, e-t)

A: Given  rt=e-tcost,e-tsint,e-t First find derivative of given point dxdt=-e-tcost-e-tsint…

Q: Find the tangent line equation to the parametric curve cos t y = sin t at t = O A. y = x+ O B. y =…

A: If the parametric equations of a curve are given variable t, then the slope of the tangent is the…

Q: The velocity of a particle moving in the xy plane is given by the parametric equations dx/dt=…

A: The given parametric equations of the particle is dxdt=-2t sin2t and dydt=2t cos2t. Evaluate the…

Q: x = 3 ln(t), y = 4t1/2, z = t3; (0, 4, 1)

A: Given Data: x=3lnt ......1y=4t1/2  ......2z=t3      ......3 x0, y0, z0=0, 4, 1   For the specified…

Q: Consider the parametric curve C defined by x = x (t) and %3D y = y (t). (a) How do you find the…

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