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Test 2 100 headers Math 5C Friday, September 28, 2012 Name_______________________________________ state and respond the questions asked below. You must show all of your work to contract credit. Mathewson 1) answer the short- answer, T/F questions. A. The vector function r(t) = t guilte t, ___________ , t describes a spiral on the stand up of a cone. B. For vector function r(t), building block tangent vector T(t) = b C. 10pts . r (t) dt is the __________________________ of a space obeisance r(t) from t = a t o t = b. a D. TRUE or FALSE: diverge is negative when piteous out of a curve. D. The rule matted for space curve C at a height is the horizontal containing unit vectors ______ and _______ E. F. TRUE or FALSE: B(t) does not need to be scaled since it is already a unit vector. v2 is an expression for the ___________________________ dower of speedup. G. TRUE or FALSE: The acceleration of a ingredient following a space cu rve lies in the normal plane. 2) Sketch the curve with the wedded vector equation, starting at t=0 . Indicate with an pointer the direction in which t increases. Be sure to include a some points to justify your graph. 8pts r(t) = romaine lettuce t, sin t, sin 5t 1  find the unit tangent vector of the given curve. 5 5 3) r(t) = 9 cosine t i + 9 sin t j - 12tk 9 9 Evaluate the integral.

4 2t 15 -i j+ 4) 2 2 )2 (8 + t 0 6pts tk dt 6pts 2 5) Find the length of the curve. (Hint: Be sure to commit one of the results from a previous problem.) r(t) = 9 cos 5 5 t i + 9 sin t j - 12tk, 9 9 6) Find the curvature of r(! t) = et cos t, et sin t, t 0 7pts 9 5 t at the point (1, 0, 0). 3 7pts 7) At what point on the curve r(t) = t3 i + 3t j + t4 k is the normal plane parallel to the plane 6x + 6y - 8z = 1? 12pts Find T, N, and B for the given space curve. 8) r(t) = 3 + 2 sin 2t i + 4 + 2 cos 2 t j + 3 tk 20pts 4 Solve the problem. Assume dynamic is ideal, launch...If you want to bewilder a full essay, order it on our website: OrderCustomPaper.com

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