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MIT18_014F10_pset5

MIT18_014F10_pset5 - IF you can fgure out the right...

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Derivatives Pset 4 (4 pts each) Due October 15 (1) Notes H.8:2 (2) Notes H.9:6,7 (3) Page 155:8 (4) We define a set A R to be dense in R if every open interval of R contains at least one element of A . Let A be a dense subset of R . Let f ( x ) be a continuous function such that f ( x ) = 0 for all x A . Prove that f ( x ) = 0 for all x R . (5) Let f ( x ) be a continuous function on [0 , 1] and consider w R . Show that there exists z [0 , 1] such that the distance between ( w, 0) and the curve y = f ( x ) is minimized by ( z, f ( z )). (Hint: Notice I’m not telling you to find the value for z , just to show it exists.
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Unformatted text preview: IF you can fgure out the right Function to use and the right theorem to reFerence, this will be quick!) (6) Page 173:7 Bonus: Notes H.10:10 1 MIT OpenCourseWare http://ocw.mit.edu 18.014 Calculus with Theory Fall 2010 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms ....
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