1. Limited time only! Sign up for a free 30min personal tutor trial with Chegg Tutors
    Dismiss Notice
Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Sequences and continuity

  1. Nov 26, 2011 #1
    If [itex]f[/itex] is continuous function and [itex](x_n)[/itex] is a sequence then [tex]x_n \to x \implies f(x_n) \to f(x)[/tex]
    The converse [tex]f(x_n) \to f(x) \implies x_n \to x[/tex] in general isn't true but why is it true, for example, if [itex]f[/itex] is arctan?
     
  2. jcsd
  3. Nov 26, 2011 #2
    Let [itex]\mbox{arctan}(u_n) \to \arctan(u) [/itex]. Write [itex] x_n = \mbox{arctan}(u_n) [/itex] and [itex] x = \mbox{arctan}(u) [/itex], so [itex] x_n \to x [/itex]. Now using [itex]x_n \to x \implies f(x_n) \to f(x)[/itex], with [itex] f [/itex] as tan gives the result. Why can you do this?
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook




Similar Discussions: Sequences and continuity
Loading...