MATH 126 Midterm: MATH 126 UW Midterm 2 Spring 14rothvossExIIans
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Dd 12:30-1:20 by bo peter a exercise possible score. All other electronic devices (including graphing calculators) are forbidden: unless otherwise indicated, your answers should be exact instead of dec- 4 is an exact answer and is preferable imal approximations. For example to its decimal approximation 0. 78: unless otherwise indicated, show your work and justify all your answers. Consider the curve~r(t) = ((t2 2)2,t4,t2): compute ~t (t) for general t. ~r (t) = (4(t2 2)t, 4t3, 2t) = (4t3 8t, 4t3, 2t) |~r (t)| = p32t6 64t4 + 68t2 = 2tp8t4 16t2 + 17. 32t6 64t4 + 68t2: show that the curve lies in the plane x y + 4z = 4. Solution: simply check that (t2 2)2 t4 + 4t2 = (t4 4t2 + 4) t4 + 4t2 = 4: find one (non-zero) vector that is parallel to ~b(1). Hint: think about what b) means for the osculating plane and for the position of the vectors ~t (t),~n(t),~b(t).
