Suppose r(t) = i+t²j+2tk. Find the length of the portion of this curve that goes from the point G, 1,2) to (9,9,6). Also, give an expression for the curvature as a function of t.

Q: Find the length of the curve below from the the point P = (1, 2) to the point Q = (8, 5). 2² = (y –…

A: The length of arc for curve y=fx from x=a to x=b is given as follows. L=∫ab1+dydx2dx The given curve…

Q: Evaluate Szdz where y traces the arc of the parabola y = x² from (1,1) to (2,4).

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Q: Find the exact length of the curve y = br (ex :/) 1) + لے سلاے ахо

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Q: Find the curvature and the radius of curvature of the curve y = x + 5x2 – 2x3 at the origin (0,0).

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Q: Find the curvature of the curve r(t) = (-5t, 3t5, 2t³) at the point t = Give your answer to 2…

A: r(t)=<-5t, 3t5,-2t3>, point, t=-1

Q: Find the curvature of the curve =.

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Q: What about the part where it has to be part of the curve r= sqrt(2cos(2theta))?

A: As per the question to evaluate the volume of a cylinder with specific geometric properties, we can…