MATH 241 Final: MATH241_ALL-SECTIONS_FALL2012_0000_FINAL_EXAM
10 Jan 2019
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. follow the instructions as to which problem goes on which answer sheet. You may use the back of the answer sheets. do not evaluate integrals or simplify answers unless indicated. Please put problem 1 on answer sheet 1: consider the vectors a = 2 -j+ 3 k and b = + j+ k. (a) find the projection of a onto b. [5 pts] (d) find the equation of the plane containing the point (1,2,3) which is parallel to both the. Please put problem 2 on answer sheet 2: (a) find the length of the curve parametrized by. [15 pts] r(t) = t3/2 +tsintj+tcostk for 0 ~ t ~ 7r. Note: if you"re careful the integrand should simplify a lot before integration. (b) "find the tangential component of acceleration for r(t). Please put problem 3 on answer sheet 3: let f(x,y,z) = xe{y2-z2). (a) find the direction of maximum increase of f at the point (1,2, -2).
