b.) show brnormal of that the unit L = t+(e-s) E of |k-s) K | K* where K és the curvature of &(s) andd T is the torslon
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- The graph y = f(x) in the x plane automatically has the parameterization x = x, y = f(x) and the vector formula r(x) = xi + f(x)j. Use this formula to demonstrate that if f is a function of x twice differentiable, then, B) Use the kappa formula in subsection a) to determine the Curvature of y = In(cos x), -pi/2 < x < pi/2. Compare your Answer with that of exercise 1. C) Demonstrate that the curvature is zero at a turning point.Suppose C is the curve given by r(t) = (3 cos(t), -3 sin(t), 4t). Show that both the curvature as well as the torsion of C are constant, and find their values.Consider points P and Q on a curve. What does it mean for the curvature at P to be less than the curvature at Q?
- Let the the position vector be R(t)=⟨−t,2cos(3t),2sin(3t)⟩. Compute the curvature κ(t).Sketch the space curve r(t) = −ti + 4tj + 3tk and find its length over the given interval [0, 1] .Suppose a point X lies in the exterior of a disk, and suppose that two lines are drawn from X tangent to the circle. If one line is tangent at Y and the other line is tangent at Z, then show that the line segment XY is congruent to the line segment XZ.