Find the length of the curve. r(t) = (9t, 3 cos(t), 3 sin(t)), -7

Q: 4. Find the moving trihedral of the curve f(t) at the indicated value: †(t) = cos? t î + sin² t ĵ…

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Q: Consider the following. x = sin(t),    y = csc(t),    0 < t < π/2 (a) Eliminate the…

A: x(t) = sin(t)y(t) =csc(t)

Q: find an equation for the line tangent to the curve at the point defined by the given value of t.…

A: To find: The equation of tangent to the curve and also find d2ydx2. Given: The functions are x=cos…

Q: 2. Let y be the curve in R° given by t (t, 2 cos t, 2 sin t) for 0 < t< 47. Compute y? ds

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Q: 1. Find the length of the curve given by e' (sin t+cos t) , yY = e'(cos t – sin t), x = 1<t< 4 .

A: The length of a parametric curve is given by L=∫abx't2+y't2dt Now, we have…

Q: Find of the curve the curve lenght from t=o to t=2M given C: P(t) = (cos 3t) î + (sin 3t) Î + ? tVt…

A: Here I am attaching image so that you understand each and every step.

Q: 1. Consider the curve C: r(t) = (t - sin t)i + (1– cos t)j, 0StS 2. %3| | (a) Find an equation of…

A: Since solve the first question for you. If you wanting any specific question to be solved then…

Q: Find the exact length of the curve. 1x2 - In(x), 1< x s 8 у3

A: Hello! Thank you for the question. We will answer the first question since the exact one wasn’t…

Q: Find the exact length of the curve (b) x = e' cos t, y= e' sint, 0<t<T

A: Length of the curve for parametric equation is given by:

Q: 2. Find the length of the curve 0<t< 2n. r(t) e'i + e' sin 2tj + e' cos 2tk,

A: From the given problem :   rt=eti+etsin2tj+etcos2tk   So,   x=et, y=etsin2t , z=etcos2t .   As we…

Q: 4) Consider the curve given by: cos(xy) = x(y – 7) – 1 %3D Find y' dx a)

A: Given function is cosxy=xy-π-1 Chain rule of differentiation states that: ddxfgx=f'gx·g'x…

Q: 3) Find the length of the curve r= cos (0/3), 0< 0 <"/4:

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Q: Find the length of the given curve: where -4 < t ≤1. r(t) = (-2t, 2 sin t, 2 cos t)

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Q: Consider the curve C shown in the figure, parameterized by: C: r(t) = (1 - cos(t), 1- sin(t), 1 +…

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Q: The slope of the tangent to the curve r = 3 sin 40 at 0 = 0 is %3D Şelect one: O a. -1 3D1 O b. 0 C.…

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Q: Find the equation of the tangent and normal to the following corce at the points indicated against…

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Q: Given the curve with parametric equation x= e* and y= In(2-r²) Find the equation of the normal to…

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Q: Find the lengths of the following curves: e. x = 8cos t + 8t sin t and y = 8 sin t – 8t cos t,…

A: Solution:Givenx=8 cost+ 8t sinty= 8 sint -8t cost,   0≤t≤π2To find the length Formulaarc…

Q: 10) Find the length of the curve r(t) = (2 sin t, 5t + 1, 2 cos t), -10 ≤ t ≤ 10 $200) il mononut…

A: Introduction: The formula for the length of the curve r(t)=(x(t),y(t),z(t)) is given by,…

Q: C) Find the arc length of the curve y-1-6x², 0≤x≤1

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Q: Find the length of the curve. r(t) : cos(8t) i + sin(8t)j + 8 In(cos(t)) k, 0 stS T/4

A: Solution is given as below:

Q: Find T,N and k for the curve: 1- r(t) = (6 sin 2t)i + (6 cos2t) j+5tk.

A: As per our guidelines we are supposed to answer only one question at a time. Kindly repost other…

Q: Find the length of the curve. r(t) = , −4 ≤ t ≤ 4

A: The length of the curve is given by  r(t) = &lt;5t, 3 cos(t), 3 sin(t)&gt; r'(t) = &lt;5, -3…

Q: Find the unit tangent of the following curve at the specified point. r(t) = 2ti + 1 · sin(2t)j+3 ·…

A: We have to find the unit tangent vector at t=pi/3

Q: Find the exact length of the curve. 43. x = t sin t , y = t cos t , 0 ≤ t ≤ 1

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Q: r = 2 cos 0,0 <o <n. 2 L = S°. dr r2 + de de.

A: Use the formula given to find length of curve.

Q: Find the exact length of the following curve y = Vx – x² + sin-'(/T).

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Q: 2. Find the length of the curve r(t) = e'i + e' sin 2tj + e' cos 2tk, 0st< 2n.

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Q: The length of the curve r(t)= [cos(t), sin(t), – 3t]with 0 <t<2n is equal to O A. 2/5 T O B. 2/6 T O…

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Q: Find the length of the curve. x = cos t y = sint 0 <t< 2n

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Q: Consider the curve where a =0 (a) Compute(t) at t = [0, +∞). (b) Find the tangent line at the point…

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Q: Find the length of the curve. r(t) = cos(3t) i + sin(3t)j + 3In(cos(t)) k, 0 stsn/4 Submit Answer

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Q: 1. Find the length of the curve r(t) = (sin 2t, cos! cos 2t) from t =0 to t 2n. %3D II

A: 1)- Given: r→t=sin 2t, cos 2t from t=0 to t=2π. The objective is to determine the length of the…

Q: Consider the following. x = sinh(t), y = cosh(t) (a) Eliminate the parameter to find a Cartesian…

A: Solution: The objective is to eliminate the parameter to find a Cartesian equation of the curve

Q: A glider is soaring upward along the helix r(t) = (cos t)i + (sin t)j + tk. How long is the glider’s…

A: Given: The path of glider as r→t=cost i^+sint j^+t k^, To find: The length of the glider's path from…

Q: Q4: Find the length of the curve r = 4 sin 0

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Q: Find an equation of the tangent to the curve at the point corresponding to the given value of the…

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Q: Find the length of the curve. r(t) = cos(4t) i + sin(4t)j + 4 In(cos(t)) k, 0 <t< t/4

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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: Given the parametric equation x=(4/5)t5/2 and y= (1/4)t4-t find the arc length of the curve on the…

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Q: Consider the following. x = sin(t), y = csc(t), 0 <t< n/2 (a) Eliminate the parameter to find a…

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Q: Find the length of the curve y = In (cos x), 0sxs 4 The length of the curve is (Type an exact…

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Q: Find the curve lenght from t=o to te2T of the given curve C: P(E) = (cos3t) î + (sin 3t) Î t ? tJE e…

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Q: Consider the following. x = sin coso), -n s 0 sa co). (a) Eliminate the parameter to find a…

A: Our objective to find the cartesian equation of the curve.

Q: 7. Find the length of the curve f(1) = In(sin r), 0 < r < a/6.

A: Topic = Application of integration

Q: Q2:Is the point lies on the curve? x*cos'y - sin y = 0, (0, 7)

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Q: Find the length of the following two-dimensional curve. 兀 r(t) = (9 cos t + 9t sin t 9 sin t-9t cos…

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Q: Find the length of the curve. x- 5 sin t+ 5t, y= 5 cos t, 0 st< O A. 5T O B. 20 O C. 10 O D. 30

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Q: Consider the following. x = 3 cosh(t), y = 2 sinh(t) (a) Eliminate the parameter to find a Cartesian…

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Q: Find the length of the curve defined by the following function for 0 <t < 2n. 7(t) = (– cos 2t)i +…

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