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Unformatted text preview: c ∈ [0 , 1] such that e c-3 c = 0. b) Use Newtons Method to approximate c with an accuracy of at least 8 decimal places. 6) a) Show that if f ( x ) is continuous at x = a and if f ( a ) > 0, then there is a δ > 0 such that f ( x ) is strictly increasing on [ a-δ,a + δ ]. b) Let f ( x ) = ± x + x 2 sin( 1 x 2 ) for x 6 = 0 for x = 0 . Show that f (0) > 0 but that there is no interval [-δ,δ ] on which f ( x ) is strictly increasing. 7) Two runners begin and ﬁnish a 100m race at exactly the same time. Show that at some point they must have been traveling with the same velocity. 2...
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This note was uploaded on 10/21/2010 for the course MATH 147 taught by Professor Wolzcuk during the Fall '09 term at Waterloo.
- Fall '09