y = 4 1 ,2 In x, 1

Q: . Find the lines that are tangent and normal to the curve at the given point x² + y? = y* - 2x,…

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Q: 48. x = e' – t, y= 4e"², 0<t<2

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Q: Find the exact length of the curve. x = et - 4t, y = 8et/2, 0≤t≤2

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Q: Find the length of the curve below from the the point P = (1, 2) to the point Q = (8, 5). 2² = (y –…

A: The length of arc for curve y=fx from x=a to x=b is given as follows. L=∫ab1+dydx2dx The given curve…

Q: Find the exact length of the curve. x = 6 + 3t, y = 9 + 2r, 0sts 5

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Q: Find the exact length of the curve. y =  1/4 x2  - 1/2 In x,   1≤ x ≤ 2

A: Consider the given curve Here the objective is to find the exact length of the given curve

Q: Find the length of the following curve. 3 2 y = 4x from x = 0 to x= 2

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Q: Find the exact length of the curve. x = 7 + 12t, y = 5 + 8t, 0sts 4

A: Given :      x=7+12t2 ,y=5+8t3 ,  0≤t≤4

Q: given curve about the x-axis. 1. y = 7x, 0 < x <1

A: Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Find the exact length of the curve over the given interval. y? = 4(x + 4)*, along 0 0.

A: we have to find the exact length of the given curve

Q: Find the exact length of the curve. x = et + e-t, y = 5 – 2t, 0 st< 4

A: Given curve: x=et+e-t, y=5-2t We have to find exact length of the curve at 0≤t≤4. Length of the…

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: Find the exact length of the curve given by Length = x = 2t², y = (0 ≤ t ≤ 4).

A: A detailed solution is given below

Q: Find the exact length of the curve. =글Vy (y-3), 16 <y< 25 X =

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Q: Find the exact length of the curve. x = 1 + 9t2, y = 8 + 6t, 0 sts 4

A: Answer is mentioned below

Q: Find the length of the curve. 29) y = 1,3. 6. 1. from x = 1 to x = 3 2х

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Q: Find the exact length of the curve. Vy (y - 3), 16 < y < 25 X =

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Q: Find the exact length of the curve. 2 3/2 y = = 12, 0<xs 1

A: Given ,y=23x32Aim: To find length of curve in [0,1]We know that…

Q: 2. Find the exact length of the curve. y = 3 ,1 < x< 2 15+51

A: Find the exact length

Q: find the length of the curve on the given interval: y = 4/3 (x+1) ^ (3/2), [0,3]

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Q: Find the exact length of the curve for the parametric equation

A: Let's say the length of the curve is L.  0 ≤ t ≤ 1 Hence, the desired length will be calculated as:

Q: Find the exact length of the curve. 36y2 = (x² – 4)³, 4 < x < 9,

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

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Q: Find the exact length of the curve. x = 4 + 6t2 y = 6 + 4t3 0 sts 4

A:

Q: Find the length of the following curve. 3 y = x* from x = 0 to x = 8

A: Given,            y=x32 from x=0 to x=8To find : The length of the curve.We know that,          The…

Q: Find the exact length of the curve. y = 5 + 2x³/2, 0≤x≤ 1 2.268 X

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Q: Find the length of the following curve. y=4x^3/2 from x=0 to x=5

A: The given curve is y=4x32 from x=0 to x=5. Compute the arc length as follows.

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. 30) x = 3 ty 3/2 - y 1/2 from x = 16 to x = 25

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Q: Find the exact length of the curve. y (y-3), 4sys 16 X =

A: use derivative for finding the exact length.

Q: Find the length of the curve defined by from = 9 to z = 10. 2 y-4lm (()²-1) =

A: find derivative

Q: Find the exact length of the curve. X = Vу (у — 3), 16 <y S 25

A: First differentiate wrt y

Q: Find the length of the arc of the curve in the given range, y3 3 4(y + 5) ' 1 x = 25y + 5y? + Osys3

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Q: Find the exact length of the curve. 36y =(x+4). 5 5 x s 6, y 20

A: Given: 36y2=(x2-4)3,  5≤x≤6,  y≥0 Arc length of curve y=f(x) on [a, b] can be calculated by…

Q: Find the length of the following curve. 3 y = 2x from x =0 to x=7

A: Given: y=2x32   from  x=0 to x=7

Q: Find the exact length of the curve y=x3/3 + 1/4x, 1 less than or equal to X less than or equal to 2

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Q: Find the exact length of the curve. 1 + x?)3/2, 0sxs2 y

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Q: Find the exact length of the curve. x = et - 4t, y = 8et/2, 0 sts 4

A: We find dx/dt and dy/dt

Q: Find the length of the curve defined by the y-axis. over the interval <r< 1 about 2.r

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Q: find the length of the curve on the given interval: y=1/3(x^2+2)^(3/2), [0, 1]

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

A: Differentiating with respect to y, we get

Q: Find the exact length of the curve. x = 8 4y2' 1sys 2

A: Given, x=y48+14y2,1≤y≤2

Q: ind the exact length of the curve. X = 8 4y2' 1sys 2

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Q: Q1. Find the length of the of the curve y = from x = 0 to x = 3.

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Q: Find the exact length of the curve. y = x2 - In(x), 1 < x < 4

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Q: For what value of c is the curve y = c/(x + 1)tangent to the line through the points (0, 3) and (5,…

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Q: Find the exact length of the curve. x = Vy (y - 3), 9 < ys 25

A: It is given that x=13yy-3, we need to find the exact length of curve.

Q: Q1. Find the length of the of the curve y= from x = 0 to x = 3.

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Q: Find the length of the curve y =1+6x?on the interval 0<x<1.

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Q: Find the exact length of the curve. x = 1 + 9t, y = 8 + 6t, 0sts 3

A: Explanation of the answer is as follows