Consider the curve C parametrized by x = 19 – t and y = 17 for all real t. %3D Then C is a O vertical line traversed in the downward direction O vertical line traversed in the upward direction O horizontal line traversed in the rightward direction O horizontal line traversed in the leftward direction

Q: Find the length of the curve y = -9+4x3/2 over the interval 0 <x <1. OAZ= (1/54) 37 /37+1 CO B I =…

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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: (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: 7. Find the length along the parametric curve defined by v(t) = (t, In(cos(t))) from t = 0 andt=.…

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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: Let m be a positive real number and C be the curve given by: r(t) = m(-cost + 3)i – m(sint + 3)j+…

A: If r(t) = (f(t) , g(t) , h(t))then L = ∫ab r→'(t)  dtwhere  r→'(t)  = f'(t)2 + g'(t)2 + h'(t)2

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A: The length of a curve means the arc of the length of a curve. The arc of the length of a curve in…

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A: First I have written a short note about line integral , along a curve in parameterization form, just…

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A: We have to check one by one here and find t value.

Q: Let C be the curve defined by 7(t) = (2+2 sin(t), 3 – 2 cos(t)) for 0 <t< L (e + 4z) dz + (2zye" +…

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Q: Express the following curves parametrically, including the interval for the parameter. 5.) The…

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

A: SOLUTION-

Q: Find a parametrization of the tangent line at the point indicated. r(t) =〈cos 2t,sin 3t〉, t = π/4

A: Given :  r(t) =〈cos 2t,sin 3t〉, t = π/4

Q: Determine all points on the parametric curve {x= 2t^3−24t y=t3−6t^2+9t−4 where the tangent slope is…

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Q: Find the length of the curve r(t) = (cos 3t, sin 3t, 2t3/2),0 sts 3. %3D

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Q: Prove that the curve y: (-,-)→ R³ is regular with factor H and determine whether the image y (t) =…

A: If γ't not equal to 0 for all t∈-π2,π2then it is regular. If γ''t=kγ't for all t∈-π2,π2 then the…

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

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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)

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A: Given: y=ln(1−x2)0≤x≤12

Q: ) Find the pdar eawation for the cartesian curve x²-y²= \x?+yz A)rsinz0=2 b)r=ュ )cos 20=1 Dr=cos2@…

A: In polar coordinates, substitute x =r sin(theta) and y= r cos(theta)

Q: Use the Midpoint Rule with N = 10, 20, 30, and 50 to approximate the given curve's length. %3D c(t)…

A: We are given the curve :c(t)=(cos t, esint) The length of the curve: s=∫02π-sin t2+(cos t esin t)2…

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Q: What is the slope at t = −2 ?

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Q: Find the length of the curve y = V- from z =1 to r = e. 3

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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: Let C denote the curve parametrized by a = cos(Tt), y = 3t, z= sin(nt), 0 <t < 1. Then S a2 + y? +…

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Q: Find the exact length of the curve. y = In(sec(x)), 0 <x< a/6

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Q: Consider the parametric curve given by (a) Find dy/dx and d²y/dx² in terms of t. dy/dx d²y/dx² = = x…

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Q: Let m be a positive real number and C be the curve given by: r(t) = mcosti – m(sint + 3)j + (5 –…

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Q: Find all values of t for which the curve given parametrically by x(t) = 4+ 2t2 y(t) = 212 + t3 , is…

A: Explained below

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: 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: Find the lengthof the curve r= a sin² (0/2), 0 s0s T, a>0

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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: 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 the curva tuie For He Curve 2+); +(6 cos 2t) + 5¢ K %3D

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Q: Find the length of parametrized curve given by  x(t) = 6t2 + 12t, y(t) = -4t3- 12t2 - 9t where t…

A: Consider the parametric curve given by: x(t)=6t2+12t and y(t)=-4t3-12t2-9t for t from 0 to 1. The…

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

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Q: Find the length of the curve C defined parametrically by C: r(t) = y(t) = e' sin t, 0<t<n e cost,…

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Q: Use Green's Theorem to evaluate / F · dř, where F = (Va + 6y, 3x + y9) C consists of the arc of the…

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Q: Find the length of the parametric curve x = sin-1t,y = In V1– t² for 0 <t<-

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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 speed of the curve F(t) = (4cos (t), 4 sin(t), 6t) at t = 3 %3| Speed =

A: Consider the curve  r(t)=&lt;4cost2,4sint2,6t&gt;

Q: Let C be the closed curve starting at (0, 1) traveling along the parabola y = (x – 1)? up to the…

A: Using Green's Theorem we solve the above question.

Q: Find F. dř for F = 5yi – (sin y)j on the curve counterclockwise around the unit circle C starting at…

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