Explain how to find the length of the curve                         r(t) = ⟨ƒ(t), g(t), h(t)⟩, for a ≤ t ≤ b.

Q: (b) Verify that Green's Theorem is true for S,3(y² – x) dx + (x² – y)dy given that the curve C is…

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Q: |-*^= 39. What is the length of the curve y = √x- between x = 0 and x = 2?

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Q: сompute f ds for the curve specified. f(x, y) = . y = r* for 1 < x < 2

A: fx,y=y3x7, y=14x4 for  1≤x≤2

Q: Find the length of the curve. 33 X = x=11t°, y= ², t,0stsv3

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Q: 6. Explain why the curve f(r) = r" + r* +x* + x +1 is always rising.

A: Given : f(x) = x7+ x5 + x3 + x + 1  To find : Explain why f(x) is always rising or increasing.…

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Q: Let C be the curve y = 8/a for 2.1 < x < 3.8.

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Q: Find the length of the curve y 2ln(x) from x 1 to x =4. %3D

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

A: Given the curve x=g(y). We need to explain the steps required to find the length of a curve between…

Q: Find the length of the curve x = 5-t, for 1 < t < 2. length = y = 3-t, z = 3t 5,

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Q: Q1. Find the length of the of the curve y -x2 X2 from x = 0 to x = 3.

A: Given curve is, y=13x32-x12 To find the length of the curve from x = 0 to x = 3

Q: Find the exact length of the curve. y2 - 16(x + 4)3, Osxs 2, y > 0

A: The given equation of the curve is y2=16x+43, 0≤x≤2, y&gt;0. The graph of this curve in the interval…

Q: Find the exact length of the curve.   y2 = 4(x + 4)3 , 0 ≤ x≤ 2 , y&gt; 0

A: Given: y2=4x+43,0≤x≤2,y&gt;0 To Find: Find the Exact length of the curve. Concept: Length of the…

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Q: Prove that the curves x2−y2=3 and xy=2 intersect at the right angle.

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

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Q: (x – 2)2 + y² = c² %3D

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Q: Find the length of the segment of the curve y = f (x) = e ^ x between the abscissa points x = 0 and…

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Q: Find the length of the curve. y= (16-x2/3)3/2 from x=1 to x=64

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Q: Prove that the following curves are intersecting with a right angle: 5y-2x+ y -x²y =0 2y+5x+ x* –…

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Q: 23. Evaluate x² c ¥4/3 ds, where C is the curve x = t², y = t°, for 1st< 2.

A: Given curve is

Q: Mike found the orthogonal line to the curve f (x) =- 3sin( zx) +1 at x=-1. In which step did he…

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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 exact length of the curve. y2 = 16(x + 4)3, osxs 2, y > 0

A: Given data:   The given expression is y2=16(x+4)3. The given limits of x is [a,b]=[0,2].   The given…

Q: Find the lengths of the curves in Exercises 1–4 1. y = (1/3)(x² + 2)³/2 from x = 0 to x = 3

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Q: Find the length of the curve y = x3/2 from x = 0 to x = 3.

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Q: Prove that the curves y2 = 4x and x2+ y2-6x+1 = 0 touch each other at the point (1,2)

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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: Sketch a curve with the following properties. 0, for x> 12

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Q: Find the value of c such that line y=3/2x+6 is tangent to the curve y=cx1/2.

A: Given,  line y=3/2x+6 is tangent to the curve y=cx1/2.

Q: |Verify that Green's Theorem is true for S,3(y2 – x) dx + (x² – y)dy given that the curve C is…

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Q: Explain why a cubic Bézier curve is completely determined by x(0), x (0), х(1), and x'(1).

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Q: Let C be the curve y = 2/r for 1.3 <x < 3.2.

A: Given that: y=2x

Q: Find the exact length of the curve. y2 = 16(x + 5)3,   0 ≤ x ≤ 1,  y &gt; 0

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Q: Find the orthogonal trajectories of the family of curves x² + Y? = R? %3D

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Q: (b) Verify that Green's Theorem is true for S,3(y² – x) dx + (x² – y)dy given that the curve C is…

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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: 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: Find the length of the curve x=e^t -t, y=e^(t/2), -8 less than or equal to t less than or equal to 3

A: The arclength for parametric curves is: L = ∫ab(dxdt)2+(dydt) Given  x=et-t, y =et2,      -8≤t≤3

Q: find and sketch the point of shortest (or longest) distance from the origin of curve…

A: We need to find and sketch the point of the shortest (or longest) distance from the origin of curve…

Q: i) Find the exact length of the curve x5 1 15 4x3 y= + 1 < x < 2,

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

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Q: . Evaluate the length of the curve, y = x/2, from x = 0 to x = 4. %3D

A: first step differentiate w.r.t to x

Q: Compute the length of the curve: f (x) = x² 2x, 0<x<2

A: Given:- f(x) =x2 -2x  To find:-  Length of curve over interval [0, 2]

Q: b The curve f(x) =ax + has inflection point at (2,27). a) -- Find the values of a and b.

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Q: IFind the exact length of the curve x= 3t -t, y=3t² ,0<t<2 ||

A: We have to find the exact length of the curve. The length of the curve is given by

Q: (b) Show that the points of inflexion of the curve y = (x- a) (x – b) lie on the | line 3x +a =4b.

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Q: A Show that the curve F(t) = lies in a plane.

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Q: find the under the curve y=7-t^2 and above the t-axis

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