A. Find the derivative of the following parametric equations as indicated. Express the final answer in its simplest form without negative exponents. T. x = 3u? – 2u ,y = 2u – 1, y"

Q: Which of the following is the equation of tangent line of the curve that is given by parametric…

A: Explanation :  Given that x= 3cost + sint y = e^2t

Q: Which of the following is the equation of tangent line of the curve that is given by parametric…

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Q: - Find dx2 for the curve defined by parametric equations x = t³ and y = e'.

A: Differentiate given parametric equation

Q: Consider the parametric curve C: x 1+cost, y= -3+2sint, 0stS (1) Sketch the curve and indicate the…

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Q: Consider the parametric equations x= cos t, y = sin t, 0sts 2n. a. What curve do the points of these…

A: Convert the parametric equations to the Cartesian equation, to find the equation of the curve . The…

Q: Which of the following is the equation of tangent line of the curve that is given by parametric…

A: Tangent to a curve at a point is a line that just touches the curve at that point and in some sense…

Q: Eliminate the parameter t to rewrite the parametric equation as a Cartesian equation. Sx(t) = 3…

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Q: Find two different sets of parametric equations for y = x2 + 6.

A: Our Aim is to find the two different sets of parametric equations for y=x2+6

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

A: The equation of a line can be obtained by using the expression y-y1=m(x-x1). Here, m is the slope of…

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

A: given parametric equations are x=1+12t , y=t3-t , z=t3+t

Q: Find the parametric equations for the tangent line to the curve æ = t3 – 1,y = to +1, z = t° at the…

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

Q: Find a Cartesian equation of the curves. 1) r= 2 sin 0 2) r = 5 csc e

A: 1) r=2sinθ2) r=5cosecθwe have to convert these curves into cartesian equations

Q: ELIMINATE THE PARAMETER IN THE PARAMETRIC EQUATIONS: x=t +1 Y = t t-1

A: Topic - equations

Q: Find the second derivative in terms of t for the parametric equations below- x=t² -t+2 y =t -3t

A: Given that, the parametric equations are x=t2-t+2 and y=t3-3t Find the first derivative in terms of…

Q: Determine the exact length of the curve for the parametric equation x = tsint and y = tcost for 0 ≤…

A: To find the exact length (arc length) of the curve for the parametric equation x=t sin(t), y=t…

Q: Which of the following is the equation of tangent line of the curve that is given by parametric…

A: Tangent line at a point will be given by slope at that particular point and one passing point for…

Q: Which of the following is the equation of tangent line of the curve that is given by parametric…

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Q: Find Dx 2 y of the following parametric equations: x= cos t y= sin t

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Q: Consider the parametric equations x= cos 1, y = sin t, 0sts 2n. a. What curve do the points of these…

A: slope = dy/dx = dy/dt /dx/dt

Q: Find the parametric equations of the tangent line LT to the curve C:r(t) = 2 cos(t)i + sin(t)j+ 2tk…

A: A parametric equation of a curve is given by: C: r(t) = 2cos(t)i + sin(t)j + 2tk Now, we have to…

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: Find the derivative of the following parametric equations as indicated. Express the final answer in…

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Q: Which of the following is the equation of tangent line of the curve that is given by parametric…

A: The equation of a tangent line passing through the point x1, y1 and slope m is y-y1=mx-x1. The slope…

Q: find the equations of the tangent and normal to the curve expressed in parametric form at the point…

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Q: Which of the following is the equation of tangent line of the curve that is given by parametric…

A: Given: The parametric equation of a curve is x=3 cos t+2 sin t ,  y=e6t To find: The equation of the…

Q: Consider the curve given by the following parametric equations: x = t2 – 3t + 3; y = t2 – 4t + 1 (a)…

A: Given that x=t2-3t+3 and y=t2-4t+1

Q: 10b. Find the parametric equations of the tangent line to the curve at t =1.

A: Given: The position vector is of a particle in space at a time t : r→(t)=<t+1,t,1t>=<x, y,…

Q: Find a set of parametric equations that represents the graph of y = 1 − x2, using each of the…

A: Given- y=1-x2 To find- Find a set of parametric equations that represents the  above graph using…

Q: Graph the parametric equations below (x(t) = t - sint ly(t) = 1- cost

A: The given parametric equations are: xt=t-sin tyt=1-cos t Find the value of x and y for multiple…

Q: The following are the parametric equations for the motion of an object: x(t) = t cos (5t² + 2), y(t)…

A: Given a parametric equation, x(t)=t cos5t2+2,  y(t)=t2 ln(-5t)

Q: Find in terms of t for each of the following parametric equations. and dx dx a x=r - 3, y =r'+1 1+3…

A: 23 b. Consider the parametric equation x=t+3t and y=t2-4t. Differentiate x=t+3t with respect to t…

Q: Determine the xy-coordinates of the points where the following parametric equations will have…

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Q: For the parametric equation shown below, determine the value of (dy/dx) and (d²y/dx²). X = 3t – 4t +…

A: a x = 3t2 -4t +2 y = t3 -2t2 + 2t -5  dy/dx and d2y/dx2 =? dx/dt  = 6t -4 d2x/dt2 = 6 dy/dt = 3t2…

Q: Which of the following is the equation of tangent line of the curve that is given by parametric…

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Q: x = 1– t- t - te [-2,2] y =t – t3

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Q: x = t? + 2t, y = 2' – 2t y. (15, 2)

A: Consider the parametric curve  x=t2+2t,                 y=2t−2t

Q: [x(t) = 3t² – 3 v(t) = 2t +1 Find the slope of the tangent to the parametric equations at t=1.

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Q: Find the equation for the following parametric equation in rectangular coordinates. x = 2t + 1 y =…

A: The solution is :

Q: To calculate the derivative dy/dx of the parametric equations x(t)= 3cost and y(t)=3sin t for…

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Q: Which one of the following equations is the equation of the tangent plane to the surface xy + xz +…

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Q: Find the equation of the tangent line(s) to the given set of parametric equations x = t² + 5t – 6 y…

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Q: Eliminate the parameter to find a Cartesian equation of the curve. x= cos 21, y=3 sint, 0sts2n

A: To find the Cartesian Equation from the given parametric equations. x = Cos2t  , y = 3Sint , 0 ≤ t ≤…

Q: Consider the parametric curve C: x=t³ + 1, y = t² – t,0 <t < 3. Find the equation of the tangent(s)…

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Q: x = +4r2 +4t +1 y =1+3 at the point P(1, 1).

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Q: Find the equation of the tangent line to the curve described by the parametric equation described…

A: To find the equation of the tangent to the curve described by parametric equation x=t4+2y=t3+t3,-2

Q: Consider the parametric equations x(1) = 1 + 3r², y(1) = 4 + 2r°, 0sts1. a. What is the length of…

A: If the parametric equations of a curve are x(t) and y(t), then the length of the curve over the…

Q: Find the Cartesian equation of the curve: x = 2cos(theta) y = 1 + sin(theta) where theta is…

A: Given that the equation of the curve, x=2cosθy=1+sinθWhere,  0≤θ&lt;π2

Q: Which of the following is the equation of tangent line of the curve that is given by parametric…

A:

Q: For the parametric equations x = cos(t), y = 3 sin(t), find the equation of the tangent line to the…

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