Show that the arclength of the graph of y=sinx on the interval [0, 2n] is equal to the circumference of the ellipse x?+ 2y? = 2. 3n 2 H

Q: Determine arc length of the graph of the equation (y-1)3  = x2 where the interval is [9,11].

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Q: Show that the curve y = x? sin 3x touches the parabolas y = x andy =-x² alternately at infinite…

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Q: Find three different parametrizations of the graph of y = x3.

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Q: Find the directrix of the parabola r = 25/(10 + 10 cos θ)

A: The parabola r=2510+10cosθ, we have to find the directrix of this given parabola.

Q: Find the equation of the parabola osculating with the function f(x)=cosx at x0=0

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Q: Find the arc length of the segment of the curve between the lines x-1 and x-16

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Q: Identify the graph generated by the parametric equationsx = t2, y = t, for -10 ≤ t ≤ 10.

A: x=t2,  y=t  for  -10≤t≤10

Q: find the arclength of y= 9-x° between its x-intercepts

A: Find the x-intercept.