17. The Cartesian equation of the curve with parametric equation x = 1+t?, y = 2t, where tis a parameter, is A y? = 4(x – 4) B y? = 4(x – 1) c y? = 4(x + 4) D y? = 4(1 – x)

Q: Consider the parametric equations y = e' +t te [1, 10] Briefly explain how you know that the curve…

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

A:

Q: 4) Find the critical points of the parametric equations x = t* - 1 y = t3 - t

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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: 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…

Q: 18. The parametric equations of a curve are given by x= at", y= 2at, where a is a constant and t a…

A: To find the equation of tangent line

Q: Find a rectangular equation for the curve with the given parametric equations. x = 2 sin(t),y = 2…

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Q: 2. Given the parametric equations: x = t + sin t,y = t- cost, findand

A: Solution...

Q: 2. Find a set of parametric equations for a particle that oscillates on the line y = 6x - 5 between…

A: formula:

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: #3. Find parametric equations for the tangent line to thể curve with parametric equations x = (sin…

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

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Q: A Cartesian equation for the parametric curve x=24sin?e, y=21cos20, n ses 31/2 is given by O…

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Q: Find the equation for the line tangent to the parametric curve: x = t^3 - 9t y = 9t^2 - t^4   at…

A: Find slope and then use equation of tangent line

Q: 2. Find parametric equations for the line tangent to the curve of intersection of the surfaces at…

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

A: Note that, the parametric equation of a line through the points x0,y0,z0 and parallel to the vector…

Q: 9. Given the parametric equations x = et and y = te-t, vt. dy (a) Find dx (b) Find dx2 d?y (c) For…

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Q: 8. Find the positive constant a(> 0) so that the parametric x = at, y = -t? is a solution to y =…

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

A: Given To find parametric equations for the tangent line to the curve with the given parametric…

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

A: Parametric equations for a line:

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

A: The tangent line to a parametric curve given by c(t)=< x(t) , y(t) , z(t) > at some point…

Q: Find parametric equations for the line tangent to the curve of intersection of the surfaces at the…

A: Here we have to find the equation of the tangent line.

Q: 6. A particle at (1,0,0) starts moving in space in such a way that its position vector at any time t…

A: The vector equation of the tangent line of the parametric curve r→t at point P is expressed by…

Q: 4. Find the slope of the curve r = cos 20 at the origin 5. A particle moves along a path whose…

A:

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: 3. A curve has parametric equations r = sin(3t) and y = cos(t) where t takes all real %3D values. dy…

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

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Q: 4) Find the critical points of the parametric equations x = t* – 1 y = t3 -t

A: Topic:- application of derivatives

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

A: Recall: sin2t+cos2t=1

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: 4. Solve for the critical points of the given parametric equation: x = t³ – 1; y = t² + t

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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: 8. Solve for the critical points of the parametric equations x = t3 – 1,y = t² +t %3D

A: The answer is found in step-2.

Q: 4) Find the critical points of the parametric equations x = 5 – In t y = t + Int

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Q: 5-6 Find the slope of the tangent to the parametric curve at the indicated point. 5. x = t? + 2t,…

A: To find the slope of the tangent to the parametric curve at the point 15,2 x=t2+2ty=2t-2t

Q: 8. The tangent line to the curve r(t) = Li+ej=t'k 2-t at the point P(1,1, -1) intersects the line…

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Q: 2. Find a set of parametric equations for a particle that oscillates on the line y = 6x – 5 between…

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Q: 31. Find parametric equations for the tangent line to the curve of intersection of the cylinders x2…

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Q: List all of the points (x,y) on the parametric curve x=t^3+4t,  y=6t^2 where the tangent line is…

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Q: 8. Solve for the critical points of the parametric equations x = t - 1,y = t² +t

A: To find the critical points of parametric curve x(t)=t2-1, y(t)=t2+t

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: 9.) a. Find the parametric equations for the tangent line to the Curve at' the Specific point. X =t°…

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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: 30. Find parametric equations for the tangent line to the curve of intersection of the cone z = x +…

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Q: 13. Consider the curve C given by the parametric equations x=2–3cos t and y = 3+2 sin t, for –sis 2…

A: Formula a) dy/dx b) y-y1 = (dy/dx)(x-x1)

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

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