johnnywup> you too!
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9:51 PM <EmeraldExplorer> I need to prove that d/dx(a(n)) = f(f sub n-1 (x))-f sub n-1 (x)) if a(n) = f(f sub n-1) ? I need to check the answer by mathematical induction.
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9:52 PM <EmeraldExplorer> 0.50c for someone who helps me correctly solve the problem
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9:53 PM <johnnywup> uh
9:54 PM <johnnywup> EmeraldExplorer: do you have a picture of the problem or something
9:54 PM <johnnywup> that notation is sorta hard to read
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9:54 PM <EmeraldExplorer> johnnywup: chrome-extension://oemmndcbldboiebfnladdacbdfmadadm/https://ay15.moodle.umn.edu/pluginfile.php/651517/mod_folder/content/0/c1-3.3.pdf?forcedownload=1
9:54 PM <EmeraldExplorer> w8 idk if that will work
9:54 PM <johnnywup> it didnt
9:55 PM <EmeraldExplorer> https://ay15.moodle.umn.edu/pluginfile.php/651517/mod_folder/content/0/c1-3.3.pdf?forcedownload=1
9:55 PM <rufsketch1> Hello everyone. If I have two circles of differing radius at two arbitrary spots on a sphere, how can I find a great bitangent to them both?
9:55 PM <mitts> requires a login
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9:56 PM <rufsketch1> how can I fine a great-arc* bitangent to them both.
9:56 PM <iijii> johnnywup: does this look about right? http://i.imgur.com/iKvkl9I.png
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9:58 PM <johnnywup> explanations basically correct yeah
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9:58 PM <johnnywup> could be worded slightly better but it works
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9:59 PM <EmeraldExplorer> johnnywup: but how do I prove it by mathematical induction I mean? That is the part i dont get...
10:00 PM <johnnywup> EmeraldExplorer: id love to help but i cant see the image youre sending me
10:00 PM <johnnywup> so yeah
10:00 PM <johnnywup> upload to imgur?
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10:00 PM <EmeraldExplorer> johnnywup: https://gyazo.com/d177d2ef91141b6400f0bfe1bda684a7
10:02 PM <johnnywup> did you get what the derivative is?
10:03 PM <EmeraldExplorer>  f(f sub n-1 (x))-f sub n-1 (x)) ?
10:03 PM <EmeraldExplorer> not really used to doing this induction with derivitave stuff
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10:04 PM <EmeraldExplorer> johnnywup: is that correct or not?
10:04 PM <johnnywup> hmmm im not sure but it seems to me that
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10:05 PM <johnnywup> its f'(f_n-1) f'(f_n-2)...f'
10:05 PM <johnnywup> but uh
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10:06 PM <johnnywup> thats what it seems like to me
10:06 PM <johnnywup> and then for induction
10:06 PM <iijii> limit (x->0)  of cos(x)/x = 1 right?
10:06 PM <EmeraldExplorer> no
10:07 PM <johnnywup> assume its true for f_n
10:07 PM <EmeraldExplorer> lim x - > 0 (cos(x)-1)/x=0 I think
10:07 PM <johnnywup> prove its true for f_n+1
10:07 PM <johnnywup> note f_n+1 = f(f_n)
10:07 PM <johnnywup> and the derivative of f(f_n)=f'(f_n)f'_n
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10:08 PM <johnnywup> but f'_n = f'(f_n-1)f'(f_n-2)...f'
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10:08 PM <johnnywup> so we get d/dx f_n+1 = f'(f_n)f'(f_n-1)f'(f_n-2)...f'
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10:08 PM <johnnywup> which is exactly what would happen if you replaced n with n+1
10:09 PM <johnnywup> so n being true implies n+1 being true so its true that d/dx f_n = f'(f_n-1)f'(f_n-2)...f'
10:09 PM <EmeraldExplorer> oh i see
10:09 PM <EmeraldExplorer> forgot chain rule :p
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10:09 PM <johnnywup> hope that was helpful
10:09 PM <johnnywup> the notation probably looks awful but hopefully you get what i mean
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10:11 PM <iijii> limit (x->0)  of cos(x)/x = 1 right?
10:11 PM <EmeraldExplorer> iijii:  lim x - > 0 (cos(x)-1)/x=0 I think
10:12 PM <iijii> r u sure EmeraldExplorer ? it's not 1?
10:12 PM <EmeraldExplorer> iijii: google
10:13 PM <johnnywup> cos(0)=1
10:13 PM <johnnywup> 1/0 != 1
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10:13 PM <johnnywup> as far as cos(x)-1 /x being 0
10:13 PM <johnnywup> think of definition of derivative
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10:13 PM <johnnywup> (cos(x)-cos(0))/(x-0)=d/dx cos(x) at 0
10:14 PM <johnnywup> derivative of cosx is -sinx
10:14 PM <johnnywup> -sin(0)=0
10:14 PM <iijii> johnnywup: EmeraldExplorer how come this look slike it's going to 1? http://imgur.com/fM763e6
10:14 PM <johnnywup> you typed cos(x)/x not sin(x)/x
10:14 PM <johnnywup> :P
10:14 PM <EmeraldExplorer> iijii: just remembering off the top of my head
New messages since you scrolled up
10:14 PM <iijii> oh lawl
10:14 PM <johnnywup> same with that limit, definition of derivative
10:15 PM <palace> What is the relationship between ergodicity,recurrence,stationarity, and irreducibility in the context of markov chains/random walks/time series?
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10:15 PM <johnnywup> sin(x)/x=[sin(x)-sin(0)]/[x-0]=d/dx sin(x) at x=0,
10:15 PM <iijii> ur right for sine = 1 cosine = 0
10:15 PM <iijii> ty
10:15 PM <johnnywup> d/dx sin(x)=cos(x)
10:15 PM <johnnywup> cos(0)=1