Given the parametric curve x = t – sin(t),y = 1 - cos (t), find an equation for the line tangent to the curve at the point defined by t =“. Also find the value of - d²y at this point and comment on concavity. dx²

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A: x=4cosθ and y=4sinθ We have to find: (1) dydx (2) d2ydx2 (3) Slope at point θ=π4 (4) Concavity at…

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A: We are authorized to answer one question at a time, since you have not mentioned which question you…

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A: Given query is to find the slope of the tangent.

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A: Find the tangent vector r't:                 r(t)=(t3-1)i +(t5+1)j +t5k Differentiate r(t):…

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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…

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A: Given that  x(θ) = sin θ − 1 and y(θ) = θ + cosθ To determine the  Find dy/dx b. Find d2y/dx2   c.…

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A: Differentiating under the sign of integral.

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A: NOTE: Refresh your page if you can't see any equations. . take derivative

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Q: A curve is defined by the parametric equations (t) = 8 cos(6t) and %3D y(t) 4 sin(-4t). Find . %3D

A: We have to find derivative

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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: Let C1 be the curve with parametric equations x = cos t, y = sint – t, where t E [0, 5). (a) Find…

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

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A: We first find dy/dx

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A: The derivative dydx defines the slope of the tangent drawn to the curve.

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A: follow next step

Q: A curve is defined by the parametric equations: x(t) = e' cost, y(t) = e' sint dy d²y Determine and…

A: The tangent line to the curve in parametric form is given as follows

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A: Given that the parametric equations of a curve is                               x = cos (t) ,   y =…

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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