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

Q: Let C be the curve y = x³ – 3x2 + 4x - 1 joining the points (1, 1) and (2, 3). Find the value of |…

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Q: Calculate the length of the curve č: [0; 1] → Rgiven by ( 글2 + 2t st2 + 2t + 5 (t):: HIN

A: The length of the given curve is given by using the formula of arc length in parametric equation as…

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

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Q: Find the length of the curve x=2t, y=3t, 0≤t≤1

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Q: Find the length of the curve: r = 5cos 0 1 2 3 4

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

A: The given curve is: r(t)=3t i+8t32 j+12t2 k ;                0≤t≤1

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 x = 1+ 3t2, y= 4+ 2t³, 0 <t< 1. Length =

A: Given curve x=1+3t2,   y=4+2t3       0≤t≤1

Q: Let C be the curve y = x³ – 3x? + 4x – 1 joining the points (1, 1) and (2, 3). Find the value of…

A: Solving the Cauchy integral using Cauchy theorem

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

A: To find the length of the given parametric curve

Q: Find the length of the curve, L. y = 16 (a + 3)", 0s s1. y> 0

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Q: Find the exact length of the curve. x = 2/3t3,  y = t2 − 2,  0 ≤ t ≤ 2

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Q: Find the length of the curve given by x(t) = 1 + 3t² ,y(t) = 4 + 2t³, 0 <t < 1.

A: xt=1+3t2yt=4+2t3 Differentiate the above equation w.r.t."t"…

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 exact length of the curve. x = 6 + 3t?, y = 2 + 2t3, 0 sts 5

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

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Q: Find the length of the curve. r(t) = 2i + t2j + t³ k, 0 sts 1 %3D

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Q: Explain the steps required to find the length of a curve x = g1y2 between y = c and y = d.

A: It is given that x=gx for c≤y≤d.

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 exact length of the curve. 1 + 1sys 2 8 4y2

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Q: Find the length of the curve r = 02 from 0 = 0 to 0 = 14.

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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

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

A: Explained below

Q: For curve r = (t, t2,t-³) %3D Does this curve go through the point (-1, 1, -1)?

A: We have to find if the given curve passes through the point (-1,1,-1).

Q: Find the length of the curve x = y2 — 2y, 0 ≤ y ≤ 2.

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Q: Find the length of the curve x = (y3/33) + (11/4y) on 3≤y≤5.

A: Consider the given curve f(y) and find the derivative w.r.t y.

Q: Find the exact length of the curve. x= (y4/8)+(1/4y2), 1&lt; y &lt; 2

A: The given function is,

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

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Q: Find the length of the curve. x = (v - 1) 3/2 from y = 16 to y = 25 O 4 61 O IK

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Q: Find the exact length of the curve. 1 Vy (v - 3), 4 < y< 16 3 X =

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Q: Find the length of the curve. x = 4t, y =t3/2,0 st s9 122 242 3 3 O 3. seçenek 4. seçenek 61 61 3 2

A: Explanation of the answer is as follows

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

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

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Q: Find the coordinates of the point in the curve y = 12x – 2y + 23 that is nearest to the point P(10,…

A: Given curve: y2=12x-2y+23 The point is  P10,4 To find: The coordinates of the point on the curve…

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

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Q: Determine the length of the curve r(t) = 4sin(3t)i + 3tj + 4cos(3t)k, 0 <t < -. 2 Give your answer…

A: Arclegth of the position vector

Q: Q.N.4 Find the length of the curve 3x = (y + 2)3/2 from y = 2 to y 3 %3D

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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) 4 it2j3k, 0 st s 1

A: Consider the curve x = 4, y = t2 and z = t3.The derivatives are

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 exact length of the curve. x =  2 3t3,      y = t2 − 2,      0 ≤ t ≤ 2

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Q: Find the length of the curve. (2^(1/2)) t i + et j + e−t k,     0 ≤ t ≤ 9

A: Given curve is rt=2t i+etj+e-tk , where 0≤t≤9 Differentiating the given curve with respect to t,we…

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

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