Sketch the curve by eliminating the parameter, and indicate the direction of increasing tat t-0. = Vi, y= 21 + 3

Q: (b) Investigate where the curve y = xy4 - x² is concave up and concave down?

A: Given curve is y=x4-x2 find the concavity of the given curve

Q: I Find the acute angle between the two curves xy = 3 and x2 = 9y

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Q: calculate |(3y-VE)ds where C is the curve

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Q: (A) Find the equation of tangent and normal to the curve 2x2 + y = 9 at (-2, –1).

A: To find the equation of tangent and equation of normal at the given curve .

Q: Use a graph to estimate the coordinates of the lowest point on the curve x = t³ - 31, y = 1² +1+1.…

A: Consider the parametric equation x=t3-3ty=t2+t+1 Sketch of the parametric equations is shown below.

Q: Find the slope and concavity of the curve at the given points. r = 1/u, u = -pi, 1

A: Solution:Given    r=1u, u=-π,1To find the slope and concavity of the curve.Formula:Slope of the…

Q: Describe the shape of the curve x = 3 cost,y = 3 sin t.

A: We have to describe the shape of the curve x=3cos(t) ,y=3sin(t)

Q: Find the slope of the tangent line to the curve - 42? – zy + y - 4 at the point (– 2, 2).

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

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Q: Find the equations of the tangent lines x = t3 − 6t, y = t2 at the point where the curve crosses…

A: To find the equations of the tangent linesx=t3-6t,y=t2 at the point where the curve crosses itself.…

Q: (b) Eliminate the parameter to find a Cartesian equation of the curve.   for  −5 ≤ y ≤ −1

A: The parametric equation of curve are x=1-t2 y=t-3

Q: I Discuss the properties of the curve and sketch fully: a) y = x² e-x 1+lnx b) y = -

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Q: verify that the given point is on the curve and findthe lines that are (a) tangent and (b) normal to…

A: We plug x=1 and y=π/2 in the given function  Since both sides are equal so (1, π/2) is on the curve…

Q: find equation for the lines that are tangent andnormal to the curve at the given point.xy + 2x - 5y…

A: Given : The equation is x y + 2x - 5y = 2 and point (3, 2).

Q: Find the slope of the tangent line to the "tilted" ellipse at the point (-1, 1). x²+ y² = xy+3 3 3…

A: To find the slope of the tangent line to the ellipse x2+y2=xy+3 at the point -1,1

Q: At what point(s) does the curve given by x = 2 − t^2, y = t^2 + 2t have a horizontal tangent?

A: Solution :- For the curve to have horizontal tangent  Put dy/dt  = 0  The whole procedure is shown…

Q: Find the slope and concavity of the curves at the given points. r = eθ, θ = 0, π

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Q: The equation of the tangent line to the curve z +y = 36, at (2,-19) is 19 y 3= (х — 2) - 19 19 19 y…

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Q: a. Determine the points where the curve 4x + 5y - y = 6 has a vertical tangent line. b. Does the…

A: a)  curve is 4x+5y2-y=6         Slope of tangent line is m=dydx    Differentiate the above equation…

Q: Consider the curve parameterized by x = 2t³ - 33t² + 180t and y = 2t³ + 33t² + 180t. At what points…

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Q: find equation for the lines that are tangent andnormal to the curve at the given point.x^3/2 +…

A: Given: x32+2y32=17    at the point (1,4)

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

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Q: The family of curves orthogonal to ye2x = c is the family of curves whose general equation is?

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Q: Use the guidelines of this section to sketch the curve   y = x e -1/x

A: The given function is y=xe-1x. Sketch the graph of the above function as shown below.

Q: Determine the point on the curve y 16 a² where the tangent line is horizontal. A (2, 12) (-2, -12)…

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

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Q: a) Sketch the curve by eliminating the parameter, and indicated the direction of increasing t. i) x…

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Q: Sketch the curve x = 3sin2t, y = 4cos2t

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

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Q: x = Vt, y = 4 - t (a) Sketch the curve by using the

A: (a) Put t=0. x=0=0y=4-t=4-0=4 So at t=0, the point on the graph is (0,4). Put t=4 x=4=2y=4-4=0 So at…

Q: C: y= 3 17 + 12 4 | +

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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 Cartesian equation of the curve: x=2 sint, y = 5 cost, -n <t<n 6. a

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Q: Find the rectangular coordinate equation for the curve x= cost and y=1-sin2t for 0 greater or equal…

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Q: At what part of the curve 2x2 + y? = 8 does it assume the highest value?

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Q: Find the angle between the curve 2y = e – x/2 and y – axis

A: Given the curve 2y =e^(-x/2) and y-axis We have find angle between curve and y-axis

Q: Q1)a) Find line that are tangent the curve x + xy - y? = 1 at the point (2,3)

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: a. Determine the points where the curve 5x + 3y - y= 5 has a vertical tangent line. b. Does the…

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Q: Find a rectangular-coordinate equation for the curve by eliminating the parameter. x = et, y = e-t

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Q: Use the guidelines of this section to sketch the curve   y = x e -x

A: Consider the given function as y=xe-x

Q: Find the points on the curve where the tangent is horizontal or vertical. r = t - 3t, y = t?- 3.

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Q: Find an equation of the tangent line to the curve 2(2² + y?)? = 25(x² – y²) (a lemniscate) at the…

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Q: a) Sketch the curve by eliminating the parameter, and indicated the direction of increasing t. i) x…

A: Since you have posted multiple questions, we solve the first part of the question, To get the…

Q: Sketch the curve and find the axis. y = Sinx; [0,] 2

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Q: s to the curve y = x* at the %3D

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Q: The equation of the tangent line to the curve a? +y = 25, at (8,-12) is. 12 (x+8) – 12 8 y = 8. y =…

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