MATH 240 Midterm: MATH 240 UPenn 240 2012A Solutions Exams
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2x + 3y + 2z = 1 x + 0y + 3z = 2. 2 3: x = 5, x = 7, x = 11, none of the above, solve the equations for x. Hint: x = 1, x = 0. If a = : x = 2. To nd the solution vector, we need only apply the inverse: x y z. This answer can easily be veri ed by substituting back into the original system: the lemniscate of gerono is parametrized by the formulas x(t) = cos t, y(t) = sin t cos t. Compute the area of the right-hand lobe (corresponding to the range of parameters . Near the end you"ll likely need to use a u-substitution. For this speci c di erential, we have p = y and q = 0, so qx py = 1. Ydx, that is, the area of a is equal to the line integral of ydx along the boundary of a.
