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Calculating Volumes of Bounded Regions (Curve, Origin and Interval)

1. Sketch the region bounded between the given curves and then find the area of each region a) {see attachment} b) Find the area of the region than contains the origin and is bounded by the line {see attachment} 2. Sketch the given region and then find the volume of the solid whose base is the given region and which has the

Question about Curve Sketching Step-by-Step

I need help using the guidelines of curve sketching to sketch y=(x^2)/((x^2)+3). The steps seem more complicated than they should be to me, and I can't seem to get anything remotely looking like a correct answer.

Intersection of Curves

Find the points of intersection (if any) of the given pair of curves and draw the graphs. Y= x^2 and y= 2x+2

Example of a non-rectifiable closed Jordan curve.

Give an example of a non-rectifiable closed Jordan curve on the interval -1<=t<=1. My thought: t + i(sin 1/t) + ????? Please advise what curve I can add to make this work. Or, if this will not work, please provide an example of a non-rectifiable closed Jordan curve on -1<=t<1.

Length of a arc

Two people 1.8m tall walk from each other until they can no longer see each other (due to the curvature of the earth which has a radius of 6378km). Assuming nothing else blocks their view, how far do they have to walk? Note. I cant get my head around how this relates to what we've lear

Curvature of the curve and torsion of the curve

Differential Geometry (I) Curves in Space Curvature of the Curve Torsion of the Curve For the curve r = ( &#8730;6 at^3, a(1+3t^2), &#8730;6 at ) Show that k = - T = 1/[a(3t^2 + 1)^2] where k = curvature of the curve, T = tors