2. For each of the following, sketch the parametrized curves. Be sure to indicate the direction of motion Before sketching, eliminate the parameter to describe the curve as a function y = f(x). (a) (t)t, y(t) = , -1

Q: Consider the following parametric curve. x = sin(8t) + cos(t), y = cos(8t) - sin(t) Find dy dx dy dx…

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Q: 1. Find an equation for the tangent plane to the surface x cos z + yře*z =4 at Po(3, –1, 0)

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Q: 1. Find the equation of the tangent line (s) to the following set of parametric equations at the…

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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: Match each of the following parametric Equations with a plane curve : x(t) = 3 + 6sinh(t). y(t) = 2…

A: We are authorized to answer three subparts at a time, so we are answering the first three subparts,…

Q: 11. Find an equation of the tangent plane to the surface Va+Vy+Vz=4 at the point P(4,1, 1). 12. Find…

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Q: For the line, x(t) = y(t): Find parametric equations for the tangent line at t = 3 for the motion of…

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Q: 3. Consider the parameteric equations for a curve C given by x(t) = cos t(1 – cost), y(t) = sin t(1…

A: Given that: xt=cost1−costyt=sint1−cost

Q: Find the length of the curve. r(t) = cos(2t) i + sin(2t) j + 2 ln cos t k,     0 ≤ t ≤ π/4

A: Consider the length of the curve is, r(t)=costi+sintj+(lncost)k Then,…

Q: 5. Given that r(t) = 3i + e* sin tj + e cos tk Find equations of the normal plane and osculation…

A: We have to  find equation of normal and oscillating plane of above curve.

Q: 4. Find the length of the curve having a parametric equation of x = a cos 3 0, y = a sin 20 from 8 =…

A: We are asked to find the length of the curve whose parametric equations are as follows:…

Q: 4) Consider the curve given by: cos(xy) = x(y – 7) – 1 %3D Find y' dx a)

A: Given function is cosxy=xy-π-1 Chain rule of differentiation states that: ddxfgx=f'gx·g'x…

Q: Find the length of the curve with parametric equations x = e' · cos t, y = e' sin t, with 0 <t <…

A: Given x = et.cos(t) y = et.sin(t)

Q: Consider the curve C shown in the figure, parameterized by: C: r(t) = (1 - cos(t), 1- sin(t), 1 +…

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Q: 2. For the parametric curve defined by: x(t) = t2 + 4t + 2 y(t) = t³ + 2t2 + 4t + 1 (a) determine…

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Q: 11. Find an equation of the tangent plane to the surface T+VG+vz = 4 at the point P(4, 1,1).

A: we have to find the tangent plane on the given surface x+y+z=4 at the point P(4, 1, 1)

Q: (2) Consider the curve given parametrically by 1=1+2/2 cost, y = tant +2/2 sin t, for dy and show…

A: This is the application of derivatives.

Q: 3. Consider the parametric curve C given by * = te', y =t + cos t. (a) Find the equation of the…

A: Given: The parametric equation of the curve C is  x=tet, y=t+cost (a) To find: The equation of…

Q: Consider the curve parametrized by x www = 1 + ln(t) and y = t¹ + 2t. dy a) First eliminate the…

A: topic - derivatives

Q: 2. Given that r(t) = 2 sin ti + 2 cos tj+ tan tk. Find the unit tangent vector T(t) at the point…

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Q: A curve is defined by the parametric equations sin Z dz, cos z dz, t> 1. X= y= Find the length of…

A: Differentiating under the sign of integral.

Q: A curve is described parametrically by x(t)=1/(t+1), y(t) =1/(t-1). Find the equation of the line…

A: Consider the curve Find the equation of the line tangent to the curve at t=2

Q: Consider the smooth parametric curve defined by the equations = t (t² − 3) = 3 (t² − 3)' X Y where…

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Q: 10. Find the exact length of the curve y = In(sec x),0 < x<T/4 %3D

A: This is a problem related to integration of the function. Based on the integral formula we will find…

Q: A curve is defined by the parametric equations sin z dz, CoS Z dz, t 2 1. y= X= Find the length of…

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Q: 7. The curve at right is given by the parametric equations t2 z = v2t. x = In t, y = Find its length…

A: Given that, x=lnt,y=t22 and z=2t. That is, r→t=lnt,t22 ,2t. It is known that, the length of the…

Q: 5. For the Parametric curve x = a(t – sint), y = a(1 – cost) where 'a' is a constant. Find y d?y at…

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Q: 1. For the parametric equations: x = 4t3, y= 2 +60t – 8t?, find: a) All values of t at which the…

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Q: а. z = t', y = ; 0 < t < 1 b. x = cos (2t), y = sin°(2t); 0 <t< 4

A: In the given question we have to find the exact length of the given curves.

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: Find the length of the curve x=1+2sin at, y=3–2 cos at, 0<t<l

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Q: The position of a particle moving in the xy-plane is given by the parametric equations x(t) =…

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Q: 9.40. Show that the 0-parameter curves on the surface x = (r cos 0)e¡ + (r sin 0)eg + f(0)eg are…

A: We have to show that the θ-parameter curves on the surface x are parallel.

Q: Find the slope of the tangent line to the parametric curve 2te x(t) y(t) at the point P(0, 1). 2t +e…

A: xt=2t etyt=2t+etAt  P 0,1,  x=0,   y=1  ∴x=0⇒2t et=0             ⇒t=0   dxdt=ddt2t et= 2 t…

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

A: Recall: sin2t+cos2t=1

Q: 2. Find the second derivative for the following set of parametric equations. = t° – 4t3 y = t?

A: We have to find the second derivative of the given equation.

Q: 1. Evaluate the length of the curve defined by the parametric equations x = cost, y=sint, z…

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Q: Given: R(t) = (cos t + t sin t) î + (sin t – t cos t) ĵ + t?k ,t>0 Find parametric equations for the…

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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: Find the length of the following curve using methods for parametric curves. x = 4 sin t y = 4 cos t…

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Q: Find the length of the arc of the curve having the parametric equations x = t³3 and y = from t = 0…

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Q: A curve is written parametrically with x and y defined as functions of t: x=t2 +1, y = 4r° +3. Find…

A: Take the derivative of x and y with respect to t then use the formula for the arc length.

Q: Find parametric equations for the tangent line at t=3 for the motion of a particle given by…

A: To work out the equation of the tangent in terms of t

Q: Given the parametric equation x=(4/5)t5/2 and y= (1/4)t4-t find the arc length of the curve on the…

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Q: 8. Find parametric equations for the tangent line to the curve r(t) = (t² +3t +2, e' cost, In(t +1)…

A: We’ll answer the first question since the exact one wasn’t specified. Please submit a new question…

Q: ) For parametric curves x = t + \t, y = t – \t,and 0 <t< 1set up an integral hat represents the…

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Q: Find an equation of the tangent(s) to the curve with parametric equations E = t cos t, y =t sin t nt…

A: follow next step

Q: Consider a curve parameterized by: c(t)=(sin^3(t),cos(t)) Compute dy/dx at the point ((sqrt(2)/4),…

A: Differentiate the given function as follows.

Q: For the curve with parametric equations x = 4 sin (t) – 1 y= 2 cos (1) + 3 dy find the point dx at…

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Q: 1. Find the tangent to the curve given by the parametric equations: X = 1/t; y= VE e-t

A: Appliaction of derivative problem