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

Q: Find the exact value of 0.049768 x³y²z ds, where C is the curve with parametric equations x = e¯t…

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

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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: 2. Compute dy dx (x² + y²)' by first changing it to polar coordinates.

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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: When is the derivative dy/dx of the parametric equations x(t)= 3cos t and y(t)=3sin t for Ost22n…

A: Let's find.

Q: 12. Given the parametric equations r(t) = 3t + 2 and y(t) = t+1 for 0 <t< 4, find the rectangular…

A: For getting the rectangular equation eliminate the t

Q: Find ď²y dx² x = 3 sin t in the parametric equation y = 3 cost 0≤t≤ 2π.

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Q: Find in the parametric equation d'y dx² x = 5 sin² t y = 2 cost 0≤t≤ 2π.

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Q: For the parametric equations: = 26e4 and y = 46et dx () dt %3D dy (ii) dt dy (ii) %3D dx

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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: 2) Graph the x, y-curve described by the parametric equation by eliminating t from the equation. x =…

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Q: 5. Find the equation of the tangent line to the curve given by the parametric equations x(t)= 3r² –…

A: We are authorized to solve only 1 question, please repost remaining questions Equation of tangent to…

Q: In three dimensions, the cylinder x? + z2 – 10x – 6z – 2 = 0 has radius k i +tj+ and the axis line…

A: Radius =6  r(t)= (5+6cos(thetha))i+tj+(3+6sin(thetha)k

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

A: Given:

Q: Given parametric equations x = 2 cos 0 and y = sin 0. d²y Then dx2 in the point (V2,) is

A: Given parametric equation is  x=2cosθ and y=sinθ

Q: dy h,p For problems 1-3 compute dx for the given set of parametric equations. and dx? 1. x = 7t2 –…

A: 1) Given that x=7t2-9t, y=t6+2t2We have to find the dydxand d2ydx2First we find…

Q: For the parametric equations: = 48e2 and y = 41et da (*) dt (6) dt %D dy (s) da %3D

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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: Find the equation of the line tangent to the graph defined by the parametric equations 3 x =t2 – 6…

A: First evaluate the point of contact by substituting 4 for t in the given functions x and y. x=432-6…

Q: Find for the parametric curve x= 2e', y= sin(1+ e') dx

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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: 13. dy/dx = 2x, У (0) 3D —1

A: Solution: dy/dx =2x  ,    y(0)=-1

Q: Solve the following. dy 1. Determine de of the parametric equations a (t) = t? – 4t and y (t) =…

A: Since you have posted multiple questions i can do first question as per our company guidelines…

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 critical points of the parametric equations x = t* – 1 y = t3 -t

A: Topic:- application of derivatives

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 defined by the parametric equations y = 4 In((t/2)² – 1) from t = 9 to…

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Q: 2 Make a graph of the parametric equations x(t) = t - 3 on the interval 0sts 4 y(t) = ) = t ³ - 5 t

A: Given parametric equations  X(t) = t2-3  Y(t) =t3-5t

Q: Draw the isoclines with their direction markers and sketch several solution curves, including the…

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Q: For the parametric equations: = 41e2 and y = 27e* dx (i) dt dy (i) dt (tit) d

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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: 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: 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 dy/dx of the parametric equations given: x= 2t² – t and y= t³ – 2t – 1

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Q: The derivative Z of the parametric equations z= 7 sin 3t and y= cos 3t is.

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Q: 10. Find the equations of the two tangent lines at the (-1,0) for the parametric curve x = 12- 2, y…

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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: Given that x(t) = log (3t) and y(t) = t² + 3, which of the following gives a Cartesian form of the…

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Q: 3. Find the equation of the tangent line to the curve C given by the parametric equations x= e', y=…

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

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Q: Solve for the critical points of the parametric equations x = t3 -1, y = t2+t

A: To find the critical points

Q: Solve for the critical points of parametric equation x=t^3-1, y=t^2+t

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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. Given the parametric equations x= 2t+ sin 2t and y=1-cos 21, where t is a parameter, dx 2)

A:

Q: x = V1 - i , y = t³ – 3t

A: We have to find derivative

Q: 3. Find the exact length of the parametric curve x = sin-1t, y = In /1 – t2, 0<t<

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Q: 26 Given the parametric equations x=4cos? r and y = 5sint. Find dy when t= dx

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Q: Consider the following parametric equations: x=t^2+5t+4, y=4t. Find dy/dx, d2y/dx2, and the line…

A: Please refer to the image below