3. Consider the curves: r 4sin e and r = 2 sin(8) + 2cos (0). =

Q: Find the lengthof the curve r = a sin² (0/2), 0 0

A:

Q: Suppose the curve C is given by the parametric equations x=1+ \t y=e' where t> 0. Find a equation of…

A: The equation of tangent line to the curve is given below

Q: 3. What is the length of the curve r = cos3 (-) where 0 < 0 <: sos

A: See the attachment

Q: Find the length of the curve r = cos(f) + sin(0), 0sOs

A: The objective is to find the length of the curve.

Q: Describe the shape of the curve x = 3 cos t, y = 3 sin t .

A: Given:

Q: = V4 cos" : – 1, y = 10 < x < 30

A:

Q: 4. Find the acute angle between the curves y = sin r and y = cos r (0 < r <) at their point of…

A: We find the point of intersection by setting them equal

Q: 3. What is the length of the curve r = cos3 (-) where 0 < 0 <- 4

A:

Q: Find the length of the curve over the given interval. r = 4 sin θ, [0, π]

A:

Q: Find the arclength of the curve a = 8 cos(3t), y = 8 sin(3t) with 0 < t<. 9

A:

Q: Find T', N and B for the curve r(t) = (2 cos(5t), 2 sin(5t), 4t) at the point t = 0

A:

Q: Show that the exact length of the curve below is y = Vr - r² – sin ¬1 (V7)

A: SOLUTION-

Q: 3. Consider the parametric curve C given by * = te', y =t + cos t. (a) Find the equation of the…

A: Given: The parametric equation of the curve C is  x=tet, y=t+cost (a) To find: The equation of…

Q: set up intergral for the length an of the Curve 3T y%3DZ0* sin cx), 04XE

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Q: Sketch the following curves 2. y = sin(x) + v3 cos(x) on [–27, 27].

A:

Q: Find the length of the curve r(t) = (cos 3t, sin 3t, 2t3/2),0 sts 3. %3D

A:

Q: The unit circle x² + y=1 can be wrriten in parametric form as x = cos(0) and y : = sino. dy and…

A: Follow the procedure given below

Q: A curve is defined by the parametric equations (t) = 8 cos(6t) and %3D y(t) 4 sin(-4t). Find . %3D

A: We have to find derivative

Q: Find the exact length of the curve. x = 7 cos(t) – cos(7t), y = 7 sin(t) – sin(7t),

A: given : formula for arc length is as below :

Q: A curve is defined by the parametric equations sin z dz, CoS Z dz, t 2 1. y= X= Find the length of…

A:

Q: Find the equations of the lines tangent and normal to the curve given by the parametric equations…

A:

Q: Eliminate the parameter to express the curve in the form y = ƒ(x) . x = cos t, y = tan t

A: Given that, x=cost, y=tant We have to eliminate the t and express curve in the form y=f(x). As we…

Q: Find the exact length of the curve. y = In(sec(x)), OsxSa/4

A: Length of a curve f(x) in interval [a,b] is given by ∫ab1+(f'(x))2dx

Q: Find the length of the curve x=cos^2t, y=sin^2t, 0≤t≤Pi.

A: In this question,we find the arc length of the curve using x=cos^2(t),y=sin^2(t),0&lt;=t&lt;=pi Arc…

Q: Find the length of the curve x=1+2sin at, y=3–2 cos at, 0<t<l

A:

Q: Sketch the regions enclosed by the given curves. y = 2 cos(5x), y 2 sin(10x), x = 0, x = 1/10 2.0…

A:

Q: Find the length of the curve cos(t) + In(tan(;t)), y= sin(t), n/4 <t < 3T/4. x = %3D Length = %3D

A:

Q: The unit circle x² + y = 1 can be wrriten in parametric form as x = cos(0) and y = sin0. dy Find and…

A: The unit circle can be written in parametric form as x=cosθ and y=sinθ We have to find dydx and the…

Q: B. Find the length of the circle of radius r defined parametrically by x = r(v1 – sin t) and y =…

A: We need to find the length of the circle which is parametrically defined as below.

Q: Suppose a curve is traced by the parametric equations 3(sin(t) + cos(t)) = x у 3 18 — 6 соs"(€) — 12…

A:

Q: A curve C has parametric equations X = tチ+1. dy (i) Find in terms oft. dx (ii) Show that there are…

A: We first find dy/dx

Q: In which direction is the curve x = -2 sin t, y = 2 cos t, for 0 ≤ t &lt; 2π, generated?

A: x = -2 sin t, y = 2 cos t Table for values of x and y: t x y 0 0 2 π 0 -2 π2 2 0 2π 0 2

Q: Find the exact length of the curve. y = 2 In(cos (÷)) Tt/3 < x <T/2

A: Here given Differentiate the given function with respect to x using the chain rule of derivative

Q: Find the exact length of the curve. x = 9 cos(t) - cos(9t), y = 9 sin(t) - sin(9r), Ostsn 9 cos (47)…

A:

Q: Find an equation of the plane tangent to the following surface at the given point. 1 sin (xyz) =

A:

Q: Find all points of intersection of the curves r = sin 0, r= sin 20

A:

Q: Compute the length of the curve where 0 ≤0 ≤ T. x = 2 cos² 0, y = 2 cos 0 sin 0,

A:

Q: Find the arclength of the curve z = 7 cos(3t), y = 7 sin(3t) with 0 < t< 12

A:

Q: Find the exact length of the curve. x = 9 cos(t) − cos(9t), y = 9 sin(t) − sin(9t), 0 ≤ t ≤ pi

A:

Q: Consider the curve C parametrized by(x, y) = (5 cos (−12t), 5 sin(−12t)), for −π/2 ≤ t ≤ π/2 What is…

A:

Q: Answer! 6. Compute yz dz + zzdy+ zydz along the curve (cos t, sin t, tan t). 0sts*

A: line integrals

Q: Consider the curve y = – In|cos(x)| as x travels from T to 6 a) Find the length of the curve.

A: Hi, since you have asked multiple questions, we will solve the first question for you. If want any…

Q: A curve is defined by the parametric equations T = sin t, y = 1 – cos t, 0<t< 27.

A: Given parametric equations is x = sin t; y = 1 - cos t, 0 ≤t≤2π b) Eliminate t and determine what…

Q: Find the lengthof the curve r= a sin (0/2), 0s 0S T, a>0

A: The formula for finding arc length is L = ∫0πr2+ drdθ2dθ, where r = a sin2(θ2)

Q: r(t) = (e-t cos t, e-t sin t, e-t)

A: Given  rt=e-tcost,e-tsint,e-t First find derivative of given point dxdt=-e-tcost-e-tsint…

Q: The unit circle x² + y=1 can be wrriten in parametric form as x = cos(0) and y = sin0. dy Find and…

A:

Q: A curve is given by parametric equations x = cos't and y= sin' t . dy d²y Find and in terms of t. dx…

A: dy/dx=(dy/dt)/(dx/dt)

Q: Consider the given curve: R(f) = (2 cos f, 12f +3,-2 sin f) Reparametrize the curve using arclength…

A:

Q: For the curve with parametric equations x = 4 sin (t) – 1 y= 2 cos (1) + 3 dy find the point dx at…

A: