DEPARTMENT OF MATHEMATICS

MATH 1051

Problem Sheet 1 - 1st Semester, 2001

Questions marked * are to be handed directly to tutors by the end of the first tutorial.

    1. Stewart p.23: 30, 31, 33, 35, 43, 44, 45, 46, 47, 49, 52, 53

    2. Stewart p.48: 35, 36, 38, 40

    3. Stewart p.425: 1, 2

    4. Stewart p.433: 1, 2

    *5. If C(t) is the amount of Carbon C14 left after time t, we have approximately C(t) = Ce-kt , where C is the original amount of C14 present and k is the decay constant. The half-life, T, is the time for the material to decay to one half of its initial amount. If k > 0.0001, what inequality must T satisfy?

    *6. If y = sin(x), 0 £ x < p /2, find tan(x) as a function of y.