Show that the curve y = x? sin 3x touches the parabolas y = x andy =-x² alternately at infinite number of points.

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

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Q: Show that the curves r = a sin 0 and r = a cos 0 intersect at right angles.

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Q: Find the length of the arc of the parabola  x^2 = 4y from x = -2  to x = 2.

A: I am attaching image so that you understand each and every step.

Q: Consider the following. tan2(0), y = sec(0), -n/2 < 0 < t/2 X = (a) Eliminate the parameter to find…

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Q: The parametric curve x= 414 + 412 + 1, y= 5t 3 – 5t has two tangent lines at the point (9, 0). Find…

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Q: Find the arclength of y = 2x + 3 on 0 < x < 3

A: Find the differentiation of the function and then substitute the function in the arc length equation…

Q: Find the equation of the tangent plane to the following surface at the given point. 4y cos (3ar 2)…

A: Given equation of surface and point is

Q: Use the IVT to prove that the curves y = x2 and y = cos x intersect.

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Q: Compute sin z dz , where a is the piece of the parabola with equation y= a?, which lies between the…

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Q: Find the cartesian equation of the curve x = 2 sin (2t) and y = 3sin (t). Graph.

A: To find the Cartesian equation of the given curve.

Q: Find the equation of the tangent line to right branch of the hyperbola π π ㅠ x = sect, y = tant, st≤…

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Q: Eliminate the parameter to find the cartesian equation of the curve: x = 2 sin 0, y = cos² 0, sos…

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Q: (a) (., Consider the curve defined by ry = In(3x + sin(y)). Use implicit differenti- ation to find…

A: Consider the given equation of the curve, xy=ln3x+siny Use the implicit differentiation,…

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: Find a Cartesian equation of the curves. 1) r= 2 sin 0 2) r = 5 csc e

A: 1) r=2sinθ2) r=5cosecθwe have to convert these curves into cartesian equations

Q: 1. Find a cartesian equation for the curve r² sin 20 = 8.

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Q: Find the arc-length of the curve y = 2x2 +3,0 <x < 1.

A: We can find the arc length as below

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

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Q: Show that the arclength of the graph of y=sinx on the interval [0, 2n] is equal to the circumference…

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Q: Graph the lemniscate curve r2 = sin 2θ in the Cartesian xy-plane

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Q: The curves r₁(t) = (5t, t², t3) and r₂(t) = (sin(t), sin(5t), 4t) intersect at the origin. Find…

A: see my solution below

Q: Find the arclength of y = 2x/2 on 1 < x < 3

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Q: Graph the curve r2 = 4 cos θ in the Cartesian xy-plane

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Q: The equation for the tanget to graph of y=sin^1(x/2) at the origin is

A: Given, y=sin1x2 Differentiate the given function with respect to x we get, dydx=cosx212 At point…

Q: Graph the curve: x = 3et cos(t),    y = 3et sin(t),    0 ≤ t ≤ π and then find the exact length of…

A: The provided parametric equation of the curve is as below

Q: Calculate the length of the curve r=a*sin(^3)(x/3) for (x(1)=0, x(2)=3pi)

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Q: The curves r1(t) = (3t, t2, t) and r2(t) = (sin(t), sin(5t), 5t) intersect at the origin. Find their…

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Q: Find the arclength of y = 4x + 3 on 0 < x < 2

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Q: ind all the tangents to the curve y cos (x %3D

A: Here we have to find the tangents on the curve y=cos(x+y)...........(1)     , -2π≤x≤2π parallel to…

Q: Find the length of the curve r = 4 – 4 sin 0

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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 = In(cos(x)), TC 0 < x<.

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Q: Use a familiar formula from geometry to find the length of the curve described and then confirm…

A: To use the geometry we will change the polar equation into the cartesian equation first.  For that,…

Q: Eliminate the parameter to find a cartesian equation of the curve. x = sin(1/2θ),  y = cos(1/2θ),…

A: x=sin12θ,  y=cos12θ

Q: Find the arclength of y = 2x/2 on 1< x < 3

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Q: Produce three isoclines with appropriate direction markers, and sketch one solution curve passing…

A: given differential equation is…

Q: Eliminate the parameter to find a Cartesian equation of the curve. x= cos 21, y=3 sint, 0sts2n

A: To find the Cartesian Equation from the given parametric equations. x = Cos2t  , y = 3Sint , 0 ≤ t ≤…

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

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

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Q: Calculate the length of the curve γ (t) = (cos(2t), sin(2t)) t ∈ [0, π].

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Q: Find the curva tuie For He Curve 2+); +(6 cos 2t) + 5¢ K %3D

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Q: Find the length of the arc of the parabola y sq = x from  ( 0, 0 )  to ( 1,1)

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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: eliminate the parameter to find a cartesian equation of the curve x= sinh(t),  y= cosh(t)

A: x=sinht,  y=cosht

Q: The parametric equations of a curve are given by 2 x = In and y = cosh-(2t). when t = 1. dx Find

A: Given,            The parametric equations of a curve are given by              x=ln2t  and…

Q: Find the arclength of the curve x 5 cos(8t), y : 5 sin(8t) with 0 <t <

A: Given: x= 5cos8t  ; y = 5sin8t     with 0≤t≤π8---------------------Aim: To find the arc lengthL of…