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(c) Prove your guess using mathematical induction. 61. (a) Show that x x d x is divergent. about 700 hours but, of course, some bulbs burn out faster than
others. Let F t be the fraction of the company’s bulbs that burn
out before t hours, so F t always lies between 0 and 1.
(a) Make a rough sketch of what you think the graph of F
might look like.
(b) What is the meaning of the derivative r t
(c) What is the value of x0 r t dt ? Why?
68. As we will see in Section 9.4, a radioactive substance decays (b) Show that
t lim y x d x tl s exponentially: The mass at time t is m t
m 0 e kt, where
m 0 is the initial mass and k is a negative constant. The mean
life M of an atom in the substance is 0 t This shows...
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This note was uploaded on 12/27/2013 for the course MATHEMATIC 135 taught by Professor Lam during the Fall '07 term at University of Toronto.
- Fall '07