a) Compute the enclosed area and length (from 0 to 2pi) of the parametric curve given by 3, 3, x = A sin 0 and y = A cos 0.

Q: By eliminating the parameter, determine the rectangular equation equivalent to the parametric…

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Q: osen y

A: Is it sen y =x

Q: Determine the x - y coordinates 5 sin²t of the points where the parametric equation y=2 cost 0≤t≤ 2π…

A: The curve has horizontal tangent where the slope is 0

Q: Q2 - A) Find the parametric equations for the line that is tangent to the given curve : r(t) = (a…

A: To find The parametric equations for the line that is tangent to the given curve

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: determine the slope of the tangent line to the polar curve r = 1+3 cos(20) at 0 6

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Q: Find where the polar function f (theta) = 6 cos(theta) has a vertical tangents over [0,2pi]

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Q: (10) Let r(t) = (e'cos 2t, e sin 2t, e2t) a) The curve lies on a quadric surface. Give the equation…

A: Given parametric equation is  rt=etcos2t,etsin2t,e2t           (i) Let us consider…

Q: Consider curve given in polar coordinates by Find the derivative r = 8 cos 0,0 ≤ 0 ≤ π/2, dr = -8…

A: We need to find out the area of the surface of revolution formed by the given function.

Q: Consider the family of curves described by the parametric equations x = a cos t + h, y = b sint + k.…

A: The parametric equations of a curve in two variables are obtained when both the variables of the…

Q: b) The length in first quadrant of the curve x/3 + y2/3 = a²/3 is given by 6ac/2 where parametric…

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Q: Find the slope of the tangent line to the polar curve r=2cos0 at O %3D 4

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Q: 7. Find all points of intersection of the r= 3sine polar curves: such that r= 1+sine

A: We equate the two equation to find solutions.

Q: Find the polar equation for the Cartesian curve x² = Or= Or T = Or= Ora 1 Or= -tan 0 2 1 2 1 sin 0…

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Q: Without using a graphing utility, show that the parametric curve r(t) = (3t cos(3t), 3t sin(3t), 3t)…

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Q: 1. The parametric equations: x = a cos³ 0 ,y = a sin³ 0 ; 0 < 0 < 2n, define a curve called an…

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Q: Find parametric equations for the surface generated by revolving the curve y = 21 sin x about the…

A: The objective here is to find the parametric equation for the surface generated by revolving the…

Q: 2 lnt and y: where 1<t<3.

A:

Q: Describe and sketch the parametric curve in R given by x = cos t, y = sin t, z = sin 2t

A: The general form of the parametric equation of the curve in three-dimensional space is given by…

Q: 2a) Find the slope of the curve represented by the parametric equations, at 0 = T/6 %3D x = 5+ 3 sec…

A: The curve given is  x=5+3sec θy=-3+4tan θ