Q: Use Theorem 10 to show that the curvature of a plane parametric
Use Theorem 10 to show that the curvature of a plane parametric curve x = f (t), y = g (f) is where the dots indicate derivatives with respect to t.
See AnswerQ: Use the formula in Exercise 42 to find the curvature.
Use the formula in Exercise 42 to find the curvature. Formula in Exercise 42: x = t2, y = t3
See AnswerQ: Use the formula in Exercise 42 to find the curvature.
Use the formula in Exercise 42 to find the curvature. Formula in Exercise 42: x = a cos wt, y = b sin wt
See AnswerQ: Use the formula in Exercise 42 to find the curvature.
Use the formula in Exercise 42 to find the curvature. Formula in Exercise 42: x = et cos t, y = et sin t
See AnswerQ: Find the vectors T, N, and B, at the
Find the vectors T, N, and B, at the given point.
See AnswerQ: Show that the curvature is related to the tangent and normal
Show that the curvature is related to the tangent and normal vectors by the equation
See AnswerQ: Use the Frenet-Serret formulas to prove each of the following
Use the Frenet-Serret formulas to prove each of the following. (Primes denote derivatives with respect to t. Start as in the proof of Theorem 10.)
See AnswerQ: Use the formula in Exercise 63(d) to find the
Use the formula in Exercise 63(d) to find the torsion of the curve Exercise 63(d):
See Answer
