Show that the exact length of the curve below is y = Vr - r² – sin ¬1 (V7)

Q: Let 2ry + T sin y = 27. a) Verify that the Po(1, 7/2) is on the given curve. b) Write down equations…

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Q: If the curve I=3+ at? y= at + bt has a tangent line y=r-4 at t 1, what is a+b? %3D

A: We have to find a+b

Q: Show that the curve y = x? sin 3x touches the parabolas y = x andy =-x² alternately at infinite…

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Q: Find the tangent line to the given circle as directed. x² + y² + 10x – 6y – 2 = 0 parallel to y =…

A: Equation of the circlex2 + y2 +10x -6y -2 = 0⇒x2 + y2 + 10x -6y -2 + 25 - 25 + 9 -9 = 0           .…

Q: = V4 cos" : – 1, y = 10 < x < 30

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Q: Use the IVT to prove that the curves y = x2 and y = cos x intersect.

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Q: Find an equation of the tangent to the curve given by = evi y = t – In(?) at the point corresponding…

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Q: The curvature of the curve 7(t)=<6t, 6t+1, sin2t) at t= 4 is

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Q: Determine whether the statement "The curve given by x = t3 and y = t2 has a horizontal tangent at…

A: For horizontal tangent dy/dx=0

Q: Calculate F.dr, where C is the curve given by ti + 123+ tk, with t = [0, 1] and F(x, y, z) = 4xei +…

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Q: the detined b is Constant. Curiature a(t) =| 1 Cost, 1 sint, o of the curve d:laa)tR? where Find

A: We are given : α(t)=1rcos t,1rsin t,0 ⇒α'(t)=-1rsin t,1rcos t,0 Now, the Unit tangent Vector is :…

Q: Set up an intergral for the length of the curve, 04X y%3DZE* sin cx), O4 XE

A: Explanation of the answer is as follows

Q: Sketch the following curves 2. y = sin(x) + v3 cos(x) on [–27, 27].

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Q: Find the exact length of the curve. x = 7 cos(t) – cos(7t), y = 7 sin(t) – sin(7t),

A: given : formula for arc length is as below :

Q: Find the tangent line(s) to the parametric curve given by a = t5 – 4t3 y = t? at (0, 4).

A: Find the tangent line(s) to the parametric curve given by x = t^5-4t^3 , y = t^2 at (0,4).

Q: Find the length of the are of the curve п x=e' sint , y=e' cost from t-0 to t=:

A: Given: x=etsint, y=et cost from t=0 to t=π2

Q: If lx + my = 1 touches the curve (ax)" + (by)" = 1, show that %3D )+) = 1.

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Q: Given F(x, y) = [arcot(/K)-(secx)* - 2y]i+ 3x-es 2021 evy and the curve C=C,UC,UC, as shown in the…

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Q: Find the speed of the cycloid c(t) = (4t − 4 sin t, 4 − 4 cost) atpoints where the tangent line is…

A: Given: c(t)=4t-4sin(t), 4-4cos(t)

Q: Find the length of the subtangent and subnormal of a point of the curve y=b sin (x/a)

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Q: Compute the length of the curve given parametrically by x=1/3t^3 and y=1/2t^2 for 0 less or equal to…

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Q: ind the are-length of the following curves: 2 for 0sts V3 (2t +1)³² y = 3

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Q: Find the exact length of the curve y = In(1 – x²), 0 Sx S

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Q: ind the points on the curve zx? + 4y? = 1 that have a horizontal tangent line.

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Q: Find the tangent line(s) to the parametric curve given by a = t¹ - 9t² and y=t² at (0, 9).

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Q: The parametric curve x(t)=t−2t6 and y(t)=t7+2t2 is given. In which case is the tangent line at the…

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Q: Find the exact length of the curve. y = In(sec(x)), 0<x< 1/3 In (2 + v 2 ) – - In (1)

A: Since you have posted 2 questions we will solve one for you please resubmit the question. Given:…

Q: Can there be a curve satisfying the following conditions? d2y/dx2 is everywhere equal to zero and,…

A: To check: The curve satisfying the given condition or not.Explanation:

Q: For the curve x=3cos(t), y=4sin(t), find the value of d^2y/dx^2 at the point where t=π/5.

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Q: (b) Verify that Green's Theorem is true for S,3(y² – x) dx + (x² – y)dy given that the curve C is…

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Q: What is the length of the curve I= cost +tsint, y=sint - tcost, (0 <t< 2n) ?

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Q: In which direction is the curve x = -2 sin t, y = 2 cos t, for 0 ≤ t &lt; 2π, generated?

A: x = -2 sin t, y = 2 cos t Table for values of x and y: t x y 0 0 2 π 0 -2 π2 2 0 2π 0 2

Q: Let a curve be parameterized by x = t³ – 9t, y =t+3 for 1< t< 2. Set up (but do not evaluate) the…

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Q: Find the length of the following curve (a) x = 2t , y = cos 4t, 0 <t<

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Q: Consider the implicitly defined curve xy? +3x2 = 4. %3D Verify that the point (1, 1) is on the…

A: Consider the following curve: xy2+3x2=4 Substitute x=1 and y=1 in the above curve:…

Q: Evaluate + 5x)dx + (ye* – 3y²)dy where C is the boundary of the curve given below. -2

A: Detailed explanation mentioned below

Q: Let Sketch the curve and find the length of this curve. r(t) = (t, 3 cost, 3 sin t), 0≤ t ≤ 2π.

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Q: Find | xdy + ydx, where C is the arc of the curve y = eª for 0 < x < 3

A: Given Data: The given integrand is: ∫Cxdy+ydx The equation of the curve is: y=ex ......1 The limit…

Q: let rit)= demti+ dsintf+? Find the length of this curve from t=0 to t = 4.

A: we have to find the length of the curve

Q: The value of f. ydx + zdy + xdz where C is the curve x = y = z = 2t? from t = 0 to t = 1 is

A: Here we have to find the value of ∫cydx+zdy+xdz where C is the curve x=y=z=2t2 from t=0 to t=1.

Q: Find the arclength of the curve y=3/2x^2/3 for x=1 to x=8.

A: Find the arclength of the curve y=3/2x^2/3 for x=1 to x=8.

Q: . Find SF dř where F(x,y,z) = (3y?e*, 6ye* -, 1+) and C is the curve F(t) = (sin t, ,2-) for 0 stsn.

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Q: he length of the curve y = sin(3X) from x = 0 to I= is given by

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

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Q: Find the lenght of the curve y = x- tnx, 1+/dy 2. dx %3D %3D

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Q: Consider a curve parameterized by: c(t)=(sin^3(t),cos(t)) Compute dy/dx at the point ((sqrt(2)/4),…

A: Differentiate the given function as follows.

Q: Find the length of the curve r(t) = for 0 ≤ t ≤ 2π Enter the exact value.

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Q: what is the length of the curve y=1-cos(x) from x=0 to x=4pi

A: Given: y=1-cosx To find: We have to find the length of the given curve from x=0 to x=4π.