State the following curve in the form of a parameter equation a. y = 1-x², z = -2 b. y²-z²=9, x =4

Q: Eliminate the parameter to find a cartesian equation of the curve. x = et,  y = e-4t

A: A curve is a two dimensional object with equation of the form y=f(x). This equation can sometimes be…

Q: Find the exact length of the curve described by the parametric equations. x = 7 + 6t2, y = 9 + 4t3,…

A: Given curve :

Q: Give the parametric curve: x = t3 - 6t2 y = t2 - 2t Find an equation for the line tangent at the…

A: We are given: x=t3-6t2y=t2-2t For Finding the equation of the tangent line , we will have to find…

Q: Find the exact length of the curve described by the parametric equations. x = 5 + 6t², y = 3 + 4t³,…

A: Find the length of the curve   x= 5+t2 ,y= 3+4t2 , 0<=t<=1 .

Q: Find the equation for the line tangent to the parametric curve: t3 – 4t 4t2 – t4 - at the points…

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Q: Consider the following. x = e', X = y = e-3t (a) Eliminate the parameter to find a Cartesian…

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Q: Find the points on the curve xy2 = 54 nearest the origin.

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Q: Sketch the following family of curves. 1. 3x + cy – 12 = 0 %3D

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Q: Find the equation of y, glven the derlvative and the Indicated polnt on the curve. dy = 2x- 1 xp

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Q: Consider the following. x = et - 4, y = e2t (a) Eliminate the parameter to find a Cartesian equation…

A: To find The cartesian equation of the curve by eliminating the parameter

Q: Sketch the curve by eliminating the parameter, and indicate the direction of increasing t att-0. x =…

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Q: Eliminate the parameter to find a Cartesian equation of the curve: x = VE ,y = 1 – t and then sketch…

A: Given,x=t...............(1)andy=1-t...................(2)differentiating both the equation w.r.t.…

Q: The cartesian equation of the curve x = VE .y 1-t is :

A: The characterstics eqaution of the curve is

Q: Given the curve y = x3 + 3x, at what point is y' = y'' ?

A: As we know that, The Power law: ddxxn=nxn-1 The sum/difference rule: f±g'=f'±g'   Given: y=x3+3x And…

Q: Consider the curve given by the equation 0 = y3 +xy +2ax + 1+x4  y'(0) = ?

A: Answer and explanation is given below

Q: Q2- Sketch the curve: y = (x+1)

A: The function given to us is  y=x(x+1)2

Q: Find the coordinates of the point where the equation y' – xy = 2 has a vertical tangent.

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Q: dy = 18yx³ dx and whose y-intercept is 4. y(x) =

A: A detailed solution is given below

Q: Sketch the curve represented by the equations x = 1/ √(t + 1) and y = t/(t+1) , t > −1 by…

A: The given parametric equations are: The given equations are in the form of a parameter t, whose…

Q: Find the slope of the curve whose parametric equation is given by y = t³ + t²+ 1/t and x = t⁴ + 3t²…

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Q: Find the exact length of the curve described by the parametric equations. x = 5 + 3t2, y = 3 + 2t,…

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Q: Sketch the following curve y f(x, y) = x² + 1

A: Given function, fx,y=yx2+1 To sketch the curve of the function.

Q: Given the curve with parametric equations, find the slope and the equation of the tangent line at…

A: Here we have to find the Slope of tangent line at indicated points . We are given parametric…

Q: dy 20 yx %3D

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Q: Determine the parameter equation of the following curve x2 + y2= 5

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Q: Give the parametric curve: x = t3-6t2 y = t2-2t Find an equation for the line tangent at the point…

A: Given parametric curves:

Q: Given the equation 2y2 – 2xy – 4y +x? = 0 of a curve, obtain the x-coordinates of each point at…

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Q: Find an equation of the curve that satisfies dy 33ya10 dæ and whose y-intercept is 4. y(x) =

A: Given: dydx=33yx10 and y-intercept is 4. To find an equation of the curve. Solution: Separating the…

Q: 7. Eliminate the parameter to find a Cartesian equation of the curve: x = Vt, y = 5 – 3t

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Q: y =(+ + +)* x = 4t + 1, 4

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Q: Find an equation of the curve that satisfies dy 20ya de and whose y-intercept is 3.

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Q: Show that the equation of the tangent to the curve = 2 (a'0, b1.0) a y at the point (a, b) is = 2.…

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Q: Y = x2 ex X- %3D

A: the given equation of the curve is: y=x2e-x we have to solve and sketch the given curve.

Q: 1 F(t) -1<t<1

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Q: The equation y? (y² – 4) = x² (x ² – 5) is known as the devil's curve. Give an equation for the…

A: Given  :

Q: Use the guidelines of this section to sketch the curve.

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Q: Eliminate the parameter to find a cartesian equation of the curve x = t4, y = ln(t)

A: A function is a relation which maps each value in its domain to exactly one value in its range. A…

Q: -Obtain the Cartesian equation of the curve by eliminating the parameter. 14) x = t - 3, y = t2 + 5…

A: To obtain the Cartesian equation of the given curve.

Q: Find the slope of the parametric curve x = -2t3 + 1, y = 3t2, for - ∞ &lt; t &lt; ∞, at the point…

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Q: Evaluate ∫с (x+y^1/2) ds, curve is given by figure 2

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Q: Evaluate (2 - xy) ds where C is the curve given below. -2 -1 -2

A: Given   ∫C2-xyds Curve C

Q: 6x 4. У3 y = х+3

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Q: Eliminate the parameter to find a Cartesian equation of the curve for −2 ≤ y ≤ 4. x = t2 − 3,…

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Q: Eliminate the parameter to find a Cartesian equation of the curve. x = t2,    y = t5

A: A curve is a two-dimensional object with equation of the form y=f(x). Curves can be parameterized to…

Q: I Discuss the properties of the curve and sketch fully: a) y = x² e-x

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Q: The given curve is rotated y = 3 - x2,

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Q: 4. (x – h)? + y² = c²

A: The solution are next step

Q: For the curve y= ax + bx? + 12x - 7, what values of a and b will make the tangents to the curve at…

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Q: analyze and trace the given curve y = x / (1 - x)2

A: To solve the following problem