MATH H2E Final: MATH H2E Final Exam
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Instructions: the only notes permitted must be hand-written on the 3x5 inch index card you will be given in class; put your name in the upper-right corner of that index card. No calculators and no checking cell phones during the exam. Your work will be graded based on clarity as well as correctness. Throughout this exam, you can assume that if a function is de ned at a point, it has all partial derivatives at that point, and they are continuous. For example d y (0, 0), but everywhere else it is a smooth vector eld. 2zzr f (x, y) da =zzs f (x, y) da. 0 f (x) dx using 5 equal-width subintervals left end: let. Brie y explain your answer. if x is irrational. m. 0 f (x) dx, f (x i ) x. lim m . ~f d~r directly from the de nition of a line integral in terms of a parameterization.
