MATH 2214 Midterm: MATH 2214 Virginia Tech 2.5 Exam
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5. a) b) f (t, y) = tan t ty1/3. 3 ty 2/3: f fails to be continuous when t is an odd multiple of /2, and f / y fails to be continuous at y = 0. The largest open rectangle is ( /2, /2) (0, ). 6. a) f (t, y) = t2 e y y2 9 b) Y e y(y2 9 + 2y) (y2 9)2. 2t2y (y2 9)2 : both f and f / y are continuous for y 6= 3. The largest rectangle is ( , ) ( 3, 3): a) f (t, y) = b) 1 cos2 y cos(2t: f and f / y fail to be continous if y or 2t is an odd multiple of /2. The largest rectangle is (3 /4, 5 /4) ( /2, /2): the principle is that if y(t) is a solution, so is y(t 1).
