(7) Find the lengths of the curve r =2/(1 - cos 0), a/2<0

Q: Eliminate the parameter to find a Cartesian equation of the curve. x=1-cos(t) y=1-sin(t)

A: We have to eliminate the parameter and find the cartesian equation.

Q: 1. Find the length of the curve given by e' (sin t+cos t) , yY = e'(cos t – sin t), x = 1<t< 4 .

A: The length of a parametric curve is given by L=∫abx't2+y't2dt Now, we have…

Q: 4. Find the length of arc of the curve x3 + y3 = 1 in the first quadrant from the point where x = to…

A: If a function f(x) is defined over an interval [a,b], then the formula for arc length is: Formulae…

Q: (4) Find the equation of the tangent line of y = /1+4 sin x at the point %3D (0,1).

A:

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

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

A:

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

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Q: Find the length of the arc of the curve y =: +e*) from x = 0 to x =2.

A: y=ex+e-x2

Q: Find the exact length of the curve  y = ln(sec(x)), 0 is less than/equal to x is less than/equal to…

A:

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

A: The expression for the arc length of the curve is: L=∫ab1+dxdy2dy Given: x=-3y32a=0 &amp; b=4 Now…

Q: Зп 2. Find the exact length of curve y = ln (cosx), * < x < n. 4

A:

Q: Find all of the points where the curve r = 2 cos (θ/3) intersects thecircle of radius √2 centered at…

A: For the point of intersection: We need to solve the two equations simultaneously: r = 2 cos (θ/3)…

Q: The tangent of the curve x^2+y^2--7 * 2xy3DO at the point (1,1), is a. y-2-х. О b. y=x-2. O С.…

A:

Q: Find the length of the curve y = ln(sec x ), x is an element of [0, pi/4]

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Q: 2 4. Find the length of arc of the curve x3 + y3 = 1 in the first quadrant from the point where x =…

A:

Q: 1. Find the equation of the tangent line on tan-'(x²y) = cos(;x²) + xy². at (V7, 0).

A: Here is the solution

Q: 2. Find the arc length of the curve y= from x-2 to xD3 16 2x2

A: The solution is given as

Q: Find the equations of the tangent lines x = 2 − π cos t, y = 2t − π sin t at the point where the…

A: Given :       x=2-πcost, y=2t-πsint

Q: 34 10- Find equation of tangent line at the point (0, T) for Cos (7x- y) %3D 4y

A: Solved below

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: 3. Find the equations of the tangent and normal lines to the curve f(x) = /2* +cos(x*) at(0,/2).…

A:

Q: 27. Show that the tangent at any point 0 on the curve x = csec 0, y = c tan is y sin 0=x-c cos 0.

A:

Q: 1. Use four equal-length Hermite curves to interpolate y = sin(x) in the interval [0, 2r].

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Q: Find the exact length of the curve. y = 6 + cosh(3x), 0s x 8 중이nh(3) sinh(3)

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Q: Find the exact length of the curve. y = ln(cos x),   0≤ x ≤ π/3

A: Formula used: L=∫ab1+dydx2dx

Q: Find the length of the curve y = ln (cos x), 0&lt;= x&lt;= pai/3

A:

Q: 3. Find the arc length of the curve 24xy y+ 48 from y-2 to y-4 1 to from

A:

Q: Find an equation of the tangent to the curve at the given point. x = cos(t) + cos(2t),    y =…

A: Given

Q: B) Find the skpe of the Ine tangen to the curve y = sin-x at the poit

A:

Q: Find the equation of the tangent line to the curve at the point (-÷5) (글 given a cos(2 y) = 0. V3 a)…

A: We need to find the equation of the line.

Q: 8. Find a parameterization of the tangent line to r(t) = (cos(t), sin(2t)) at the point

A:

Q: 5. Find the length of the arc for x = 3 - Jy from y = 0 to y = 4

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Q: 4- Find the question of the that is tangent to the curve y=-3 cos2x at x= π/6. Express with exact…

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Q: 1. Find the length of the curve r(t) = (sin 2t, cos 2t) from t 0 to t= 2n. CoS %3D

A: Since you have posted multiple question in this question which are not interlinked so i have solved…

Q: Find the length of the curve y=In (cos x), -≤x≤0. The length of the curve is. (Type an exact…

A:

Q: 5. Determine the equation of the curve whose tangent line at any point (x, y) is e* – sinx and…

A: We need to find equation of curve.

Q: Find the exact length of the cur curve. y = Vx- x2 + - sin (V)

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Q: 1- Find the equation of the tangent to the curve y = 2 sinx+ cos2x at the point x =a. 2- Find the…

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Q: Find the length of the arc of the curve x2 + y2 = 64 from x = -1 to x = -3, in the second quadrant

A: The curve in the second quadrant can be represented as, x2+y2=64y=64-x2   The derivative of the…

Q: 4. Find the arc length of the curve x=y+y from y-1 to y-4

A:

Q: Find the exact length of the curve defined by x = 3 cos t – cos 3t and y = 3 sin t – sin 3t on the…

A:

Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time…

A: Given : x = cos2ty = cos t0 ≤ t ≤ 4π

Q: Find the slope of the line tangent to the curve r = cos(30) at 0 4

A: To determine the slope of the tangent lines.

Q: Find the distance traveled by a particle with position (x, y) as tvaries in the given time interval.…

A:

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: find the line tangent to the curve y=cos(x) at the point (π/4, 1/√2)

A:

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

A:

Q: 1- Find the equation of the tangent to the curve y= 2 sin x+ cos2x at the point x = n. 2- Find the…

A: As per our guidelines we are supposed to answer only one question.Kindly repost other question as…

Q: 1. Find the arc length of the curve f(x) = 3 4 (x + 2)2 on the interval [0, 4]. 3

A: Find the arc length

Q: what is the length of the curve y=1-cos(x) from x=0 to x=4pi

A: The given curve is  y = 1 - cosx dydx=0 - (-sinx)  =sinx