Use the comparison theorem to investigate whether the spiral r=1/θ starting at θ= 2π and going on forever has infinite or finite length.

Q: Find the points on the cardioid r = 1−cosθ at which there is a horizontal tangent line, a vertical…

A: Consider the given: r=1−cosθWrite the cartesian…

Q: Find an arc length parametrization of the line y = 2x – 6 %3D |

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Q: Find the arc length of y³ + y = x² + 6x on the interval [-5, –1].

A: Since the given graph is in implicit form (we can not find the explicit value of y in terms of…

Q: Set up an intergal of the Curve for the length 3T Y%3DZE* sin (x), O4 xE 2

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Q: Find the arc length of the curve y = (x² – 8 In(x)) from x 2 to x = 5. |

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Q: Find the arclength of y = 2x3/2 on the interval x is greater than or equal to 1 and less than or…

A: Equation of given curve is y=2x32 Differentiate with respect to x. dydx=232x32-1=3x

Q: Find the arc length of the curve y = from x=2 to x=3 2x2 16

A: Use arc length formula

Q: Find a parametrization for the curve y = Vx with terminal point (0, 0) using the angle 0 in the…

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Q: Calculate the arc length of the curve f(x)=(2/3)(x²+1)ª2) in the interval [–1,1]

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Q: Find the arc length of the curve y 1 on the interval [1, 2]. %3D 4x2

A: Given:    y = x4/8 + 1/4x2   Interval : [ 1 , 2 ]

Q: Find the arclength of y = sin (x) on the interval [0, a]. %3D

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Q: . Sketch the curve parametrized by r(t) = (ltl + t, ltl - t)

A: The given curve is rt=t+t, t-t. Sketch the graph of the above curve as shown below.

Q: Compute the arclength of the following curves. (y-1)³ =x², for 0 <x< 5 а.

A: We have to compute the arc length for the function y-13=x2, for 0≤x≤5.

Q: Find the arc length of f(x) = () (x² + 2)z on the interval [0,9] %3D

A: (6) Given function is fx=13x2+232 and interval is 0,9. We have to find the arc length of fx=13x2+232…

Q: Find the arc length of the curve f = vx from x = 0 to x = 4.

A: Consider the given function. f=x Find the derivative of the function. f'x=12x The arc length formula…

Q: Find the derivative dydx of the hyperbolic spiral r=aθ.

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Q: Find an equation for the tangent plane to the surface z + 5 = xy° cos(z) at the point (5, 1, 0).

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Q: Find the speed of the cycloid c(t) = (2t – 2 sin t, 2 – 2 cos t) at points where the tangent line is…

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Q: Find the arc length (8) of the curve 7 (t) = ( – 2e*, – 4e*, – 2e*) fo %3D c - - -

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

Q: Evaluate F. dī where F = , and C' is the circle of - counterclockwise direction.

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Q: Find the speed of the cycloid c(t) = (4t − 4 sin t, 4 − 4 cost) atpoints where the tangent line is…

A: Given: c(t)=4t-4sin(t), 4-4cos(t)

Q: Find the arc length of the curve y In(cosa) from = 0 to 2/4.

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Q: Compute the length of the curve given parametrically by x=1/3t^3 and y=1/2t^2 for 0 less or equal to…

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Q: Find the arc length of y³ + y = x² + 6x on the interval [-5,–1].

A: The arc length, L of a function, x=f(y) in the interval [a,b] is calculated using the formula below.…

Q: Find a parametrization for the line through the point (a, b) having slope m.

A: Given that slope = m , this can be written as &lt;1,m&gt; vector. And point= (a,b)

Q: Show that the tangent line at a point P = (x0, y0) on the hyperbola(x/a)2−(y/b)2= 1 has equation Ax…

A: Given equation of hyperbola  x2a2-y2b2=1 and given point is P=xo,yo. Since hyperbola is passing…

Q: Compute the arc length of the indicated portion of the curve: 7(1) = (7 +2r²)î + (21² – 4)ĵ + (7 –…

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Q: Evaluate the line integral (2 - u) dz + (3 + æ) dy] where C is the parabolic arc = a² from (0, 0) to…

A: We have to evaluate the line integral.

Q: Find the exact value of arc length of the semicubical parabola y2 = x³ between the points (1,1) and…

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Q: Find the arclength of the curve y = x – In x if < y< -1. Do not simplify your answer for this…

A: Given: y=18x2−ln⁡x if 18≤y≤e28−1 ⇒f(x)=18x2−ln⁡x if 1≤x≤e The arc length of the portion of the graph…

Q: (a) Obtain the equation of the tangent plane and the condition for tangency to the conicoid Ar? +…

A: Conicoid given is- Ax2+By2+cz2=1 at the point (α,β,γ) We have to obtain the equation of the tangent…

Q: The area of the rotational surface resulting from rotating x² + y2 = a² about the x axis is? the arc…

A: Given : x2 + y2 = a2

Q: From Rogawski ET 2e section 8.1, exercise 11. Approximate the arc length of the curve y = i x4 over…

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Q: Find the arc length of the curve x = Length = -2y³/2 from y = 0 to y = 10.

A: See the details solution in below

Q: Find an equation for the tangent plane to the surface z + 5 = xy" cos (2) at the point (5, 1, 0)

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Q: ..... The area of the surface generated by revolving the curve x = 1 cos (2t), y = 7+ -sin (2t) on…

A: Follow 2nd and 3rd step.

Q: Pls help ASAP

A: Solve the following

Q: Find the arc length of the curve S Vsect – 1 dt - sys x%3D 4

A: The given function of curve is x=∫0ysec4t-1dt To find the arc length of the curve

Q: Find the length of the following three-dimensional curve. r(t) = (6 + 3t,5 – 3t, - 1+2t), for 1sts6…

A: The length of the curve rt=ft,gt,ht in the interval a≤t≤b is given by L=∫abf't2+g't2+h't2dt. The…

Q: Find an equation for the tangent plane to the surface z +4 = ry" cos(2) at the point (4, 1, 0).

A: Use the partial differentiation for finding the tangent plane.

Q: Let curve C be the arc of x2 + y2 = 16 traversed once counterclockwise from (0, 4) to (0, -4). Let…

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Q: Find the arc length over the domain 0<t<5 7t 1 10) x= V-7t – 2, y=- + | 4 2

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Q: Use Green's Theorem to evaluate / F · dř, where F = (Va + 6y, 3x + y9) C consists of the arc of the…

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Q: On the surface z =, in what direction is z increasing most rapidly when x =1 and y = 2.

A: A function z=f(x,y) increases most rapidly, at a point (a,b) , in the direction of the gradient…

Q: Calculate the arc :length of the curve y = In(2x + 1) over the interval

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Q: The line integral (23 (x° + y°) ds, where C is the arc of the parabola y = x2 from (0,0) to (2, 4),…

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Q: 3 dz where C, is the top half of circle with radius (b) Compute the upper bound of 2,

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Q: Consider the parametric curve: X = = 7et y = 3t5 Which integral gives the arc length of the curve…

A: I am going to solve the problem by using some simple calculus to get the required result of the…