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(1) Find the length of the curve that is the graph of 7(t) = (t, 2t + 1, 2753/2) from (0, 1,0) to (4, 9,
(1) Find the length of the curve that is the graph of 7"(t) = (t, 2t + 1, 2753/2) from (0, 1,0) to (4, 9, 16). Round the answer to the nearest hundredth. 2 Hint: /\\/mx+bda:= 3m(mx+b)3/2+C. (2) Find the arc length of the curve that is the graph of (t, (at + e_*)/2) from (0,1) to (In (2), 1.25). Round to the nearest hundredth. et_et 2 1+62t_2+e2t_e2t+2+e2t_ et+et 2 _ 4 _ 4 _ 2 (3) The circle of best-t to a space curve C' at a point P has a radius that is % Where n is the curvature of C at P. Find the radius of the circle of best t to the ellipse 51:2 + 4y2 = 4 at (x/g, 1/2). Round to the nearest hundredth. Hint: 1 + ( Hint: Use as = 2 cos (t) and y = sin (t) to parameterize the curve (and put in mm space by adding a z-component of 0)
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