MATH 317 Midterm: MATH 317 2011 Winter Test 1
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For this question only, no explanation or justi cation is needed, and no credit will be given for an incorrect answer. (there are no typos in this question. answer. ) If f = p i + qj + rk is a vector eld on r3 such that p, q, r have continuous rst order derivatives, and if curl f = 0 everywhere on r3, then f is conservative. Every closed surface s in r3 is orientable. (recall that s is closed if it is the boundary of a solid region e. ) A curve in r3 is given by the vector equation r(t) = h2t cos t, 2t sin t, (a) (6 marks) find the length of the curve between t = 0 and t = 2. t3. 3 i. (b) (6 marks) find the parametric equations of the tangent line to the curve at t = .
