Problem. Find the second derivative of y with respect to x from the parametric equations given. 1. x = 1+ t²; y = 4t – 3 x =y = = 4t2 – 4t +1 2.

Q: 1.1 Find all the points on the curve x²y² + xy = 2 dy if y = x sin() dx 1.2 Find

A: Note the result : The equation represent a equation of rectangular hyperbola .The points on the…

Q: 1. Find the second derivative of the parametric equations_x = a cost and y = b sin t

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Q: Find dy/dx and d²y/dx2, and find the slope and concavity (if possible) at the given value of the…

A: We are given the parametric equations: x=6cosθy=6sinθ We know that the derivative of  cosa=-sina and…

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

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Q: From the two parametric equations below, find dy dx x = (2 − 3t)/ (1 + t) , y =(3 + 2t)/(1 + t)

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Q: Find dy/dx and džy/dx2, and find the slope and concavity (if possible) at the given value of the…

A: The answer is found in step-2

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. For the parametric equation shown below, determine the value of (dy/dx) and (d²y/dx²). x = 3t? –…

A: Since the student has posted multiple questions and does not mention any specific question, so we…

Q: Find and simplify dy/dx and d2y/dx2, and find the slope and concavity (if possible) at the given…

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Q: 1.) Given the parametric equations: x=t'- 1 and y=f+t, find the 1ª and 2nd derivatives.

A: We will find the derivatives.

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

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Q: Find dy/dx and dy/dx, and find the slope and concavity (if possible) at the given value of the…

A: Given: The parametric equation are: x=6cosθ        ... (1)y=6sinθ         ... (2)

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: 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 dy/dx and d2 y/dx2 , and find the slope and concavity (if possible) at the given value of the…

A: Given, x = cos3 θ, y = sin3 θ Parameter θ = π/4

Q: 7. Find the first derivative of y with respect to x of the following parametric equations. x = 1 +…

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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: 2.) Given the parametric equations x=cos3t and y=sin3t. Find the equation of the normal line at the…

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Q: Match the given parametric equations with one of the parametric curves. x-3- sint, y = 5+ cost O A.

A: To sketch the given parametric equation :- x = 3 -sin t  and  y = 5+cos t

Q: The derivative I of the parametric equations and y=5vt is

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Q: Eliminate the parameter from the parametric equations: x = 3 sin t y = 2+ cos t The resulting…

A: Given :                Consider the parametric equations :                       x = 3 sin t…

Q: 3. Find the second derivative for the following set of parametric equations a. x = sqrt(t) , y = 2t…

A: We have to find te second derivative.

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

A: Topic:- application of derivatives

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

A: Here, the given parametric equation of the curve is: r(t)=(x(t),y(t),z(t)) where x=6et, y=t e2t, z=t…

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: Find the First and Second derivatives of y with respect to x from parametric equations. a). x=3 (t…

A: x = 3 t + 22   and y = 9 t2 - 5⇒dxdt = 3 ×2 ×( t + 2)  , dydt = 18 t        Hence dydx = 18 t 6 ( t…

Q: 00 1. 2. 3. Match the equations of the parametric curve to the graph. x = 3 sin t у %3D 2 сos t 1. x…

A: Here the equations form of ellipse.

Q: For the parametric equations: x= 39e and y = 16e dx (i) dt dy (ii) dt dy (iii) dx || ||

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Q: a)lim              (e^-x)(x^2+sinh(x+2))    x->∞   b) Find the point where the tangent to the…

A: find limit solve the parametric equation

Q: (ii) Find for the parametric equations dx2 dy x =t – sint, y = 1 – cost

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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: i- y' + 2y 4 cos 2x. yT) = 3 (using Bernoulli Equation) %3D %3D

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Q: Find the 1st and 2nd derivatives of y with respect to x from parametric equations. a). x=3 (t + 2)…

A: First differentiate x and y wrt t then divide

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

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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: For the parametric equations: * = 22e2t and y = 3e3* da (*) dt dy (é) dt dy (á) da

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Q: dx and 3. Given the following parametric equation: =3t^2, =t^3+4. Determine without eliminating…

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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: x= et cos t y=et sin t given the parametric equation, solve its dy/dx and d2y/dx2

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Q: d) Find the slope of the parametric equations x=2+3sin and y=0-cose at 0=

A: Given: x=2+3cosθ and y=θ-cosθ   As we know that; The slope of the tangent line to the given curve is…

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

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Q: The parametric equations for the paths of two projectiles are given. At what rate is the distance…

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Q: Find the cartesian equation of the curve

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Q: 1. Find and Y and simplify whenever possible. d²y dx dx2 Given parametric equations: x = t3 +1, y =…

A: Since, you have asked multiple questions, we will solve the first question as per company…

Q: Q2: Find parametric equations of the line tangent to the graph of r(1) at the point where t= to.…

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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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