Find the length of the curve. r(t) = 3ti + 8t3/2j+ 12t2 k, 0 sts 1

Q: 48. x = e' – t, y= 4e"², 0<t<2

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Q: Find the length of the curve. r(t) 4t, t2, ostsi

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Q: Find the length of the curve. 8t3/2j + 3t2 k, r(t) = 12ti + 0 <t< 1 %D

A: Consider the provided curve,

Q: Find the exact length of the curve. y4 1 X = 8 1sy< 3 4y2"

A: Here the formula of length of the curve is:

Q: Find the exact length of the curve x = 5 + 12t? for 0 <t <1 y = 6 + 8t3

A: The objective is to find the exact length of the curve x=5+12t2, y=6+8t3 for 0≤t≤1 Now, dxdt=24t and…

Q: x = 12t°, y = 18t², 0 sts v8 X= The length of the curve x = 12t°, y = 18t on 0sts V8 is

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Q: Find the length of the curve. r(t) = √√2ti + etj+ek, 0≤t≤7

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Q: Find the length of the curve: 7= Scos 4. t2.

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Q: V3 1. Find the exact length of the curve: r(t) = , 0sts: 2 2 6.

A: SOLUTION-

Q: Find the length of the curve. x = 4t, y =- 3/2,0st s9 0 st 122 3

A: Arc length of the given curve

Q: Find the exact length of the curve. x = et − 9t,    y = 12et/2,    0 ≤ t ≤ 2

A: Note that:Arc length formula = ∫abdxdt2+dxdt2 dt                   where , a≤t≤b       Given,…

Q: 3t? Find the length of the curve x = t, y 2 osts 13. 3 =

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Q: Find the length of the curve. r(t) = 4t, t2, t3,     0 ≤ t ≤ 1

A: To find the length of the given parametric curve

Q: Find 2"dz for the case of z(= a) # z(= b), and when the curve is closed, that is when a b.

A: Note: We are not given any specification of n and the curve C. So, we have taken various cases here.…

Q: Find the exact length of the curve. y = x3/2, osxs 6 3

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Q: nd the length of the given curve. 3y2/3 = 3y43 32 X = -216 < y < 125 -

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Q: 3. Find the length of the curve r = e® for 0ses 2n.

A: Given polar curv er=eθ   ; 0≤θ≤2π

Q: Find N(t) and N(1) for the curve represented by r(t) = 3ti + 2t2j.

A: Given Curve  r(t)=3ti+2t2j We have to find N(t) and N(1) As we know that, Normal Vector is defined…

Q: Find the length of the curve. V2 ti + e'j + e-tk, 0 <t< 8

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Q: Find the length of the curve. r(t) = (4t, 0 <ts 1

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Q: Find the length of the curve. r(t) 4t, t², Osts1

A: To find arc length of curve

Q: Find the length of the curve. r(t) = 4ti + 8t3/2j + 9t2 k, 0st<1 %3D

A: Please see the answer below

Q: d the exact length of the curve. y = 1 + 8x3/2, Osxs1

A:

Q: Find the length of the curve r (t) = i + 6t°j + 2t°k, 0 <t < V1 L =

A: We will find the length of curve.

Q: z(t) = t² + 26t - 15 y(t) = t² + 26t – 10 %3D s the length of the segment of the curve between t = 0…

A: Explanation and solutions is given below....

Q: Find the length of the curve. x = t^3 - 6t^2, y = t^3 + 6t^2 , 0 … t … 1

A: Given,       x=t3-6t2, y=t3+6t2

Q: Find the length of the curve. r(t)=(8t,t^2,(1/12)t^3),0 (less than or equal to) t (less than or…

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Q: Find the length of one branch of the curve ay? = x3 from x = 0 and x = 5a. 4.

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Q: Find the length of the curve r(t) = (1,t2, t³). 0<t < 1.

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Q: Find the length of the indicated portion of the curve. r(t) = (1 + 4t)i + (1 + 8t)j + (2 – 2t)k, –…

A: To find the length of the indicated portion of the curve.rt=1+4ti+1+8tj+2-2tk, -1≤t≤0

Q: Find the length of the curve. r(t) = 8i + t2j + t³ k, 0sts 1

A:

Q: x(t) = t² + 2t – 3 %3D y(t) = t² + 2t – 30 What is the length of the segment of the curve between t…

A: Given parametric curve is xt=t2+2t−3 and yt=t2+2t−30. We have to find the length of the segment of…

Q: . Find the length of the curve C : r(t) = (4t, t2 – In(t²)), 1<t< 4.

A: Explained below

Q: 3t2 Find the length of the curve: x = t°, y = ;0<t < V168

A: As per bartleby guidelines for more than one question, only 1st one is to be answered. Please upload…

Q: Find the length of the curve 6t, t2, 13 0 st s1 r(t)

A: Given:

Q: consider a curve r(t) = 2t³ i+ 2t j+v6t² k calculate the length of the curve in the interval 0 st 3

A:

Q: Find the length of the curve. 2ti + e*j + e-tk, 0 <ts 8

A: Consider the curve:rt=2ti+etj+e−tkrt=2t,et,e−t0≤t≤8 Find the length of curve:…

Q: Find the length of the curve. r (t) = 9ti + 12tj+9t°k,0 < t< 3

A: Given r(t)=9t i +12t^3/2 j+9t^2 k Length of the curve =intergration|r'(t)|dt

Q: Find the length of the curve. r(t) = 8 i + t2 j + t3 k,    0 ≤ t ≤ 1

A: Given:

Q: Find the length of the curve 7 (t) (9 In(t), 4t?, 12t) for 1 <t < 6

A: The given curve is r→t=9lnt, 4t2, 12t for 1≤t≤6 We have to find the length of this curve.

Q: Find the length of the curve: r(t) = , t=[0,1]

A:

Q: Find the exact length of the loop of the curve = 3t – t°, y = 3t2 -

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Q: 1 Find the arclength of the curvec= 3. twith 5 <t <7. 2

A: and the given interval is  so lower and upper limit is

Q: Find the length of the curve 7(t) = (9t2, In(t), 6t) for 1 < t < 3

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Q: Let Q = 4x? + 6xy+ 4y². The points on the curve Q = 7 which are closest to the origin are:

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Q: Find the length of the curve. r (t) = v2ti + e'j+e-*k, 0 < t < 5 L =

A: first we calculate the derivative for each component of given vector we get,        r'(t) = √2 i +…

Q: Find the length of the curve r(t) = 6t°i – 2t³j – 3t³k from t = 1 to t = 2.

A:

Q: The length of the curve z=z(t)=5e", Ostsa is а) 12л b) л c) 157 d) 2

A: Sol :-                Are length in (a,b) if functions are                               x(t) , and…

Q: Find the length of the curve. r(t) = ( 6t, t2, 3 Ostsi

A: We find r'(t) using the power rule

Q: Find the length of the curve. r(t) = ( 8t, t², ostsi

A: The required length of the curve is 97/12 units.