Solve $f(x+1)-f(x)=x*\sin(x) $


closed as off-topic by ArsenBerk, Leucippus, YiFan, Sil, Shogun Jun 9 at 21:28

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  • $\begingroup$ What have you tried so far? $\endgroup$ – ArsenBerk Jun 9 at 19:46
  • $\begingroup$ @ArsenBerk calculus of finite differences $\endgroup$ – MorrisonFJ Jun 9 at 19:48

Take any function $f(x)$ defined on $[0,1)$ and then continue to all $x$ using the equation.

  • 1
    $\begingroup$ Bonus: If $f$ is continuous on $[0,1)$ and $\lim_{x\to1^-}f(x)=f(0)$, then the continuoation will be continuous on all of $\Bbb R$. $\endgroup$ – Hagen von Eitzen Jun 9 at 20:14
  • $\begingroup$ @HagenvonEitzen but $ f(x)=1/4 csc^2(1/2) (sin(x)-x (sin(1-x)+sin(x)))$ . I don't know how to come to this decision $\endgroup$ – MorrisonFJ Jun 9 at 20:17
  • $\begingroup$ @colt_browning but f(x)=1/4csc2(1/2)(sin(x)−x(sin(1−x)+sin(x))) . I don't know how to come to this decision $\endgroup$ – MorrisonFJ Jun 9 at 20:30
  • $\begingroup$ @MorrisonFJ Why do you think it's true? Because it's the answer given in the textbook? Well, if this is known to be the correct answer, then the question is apparently missing something. Perhaps the condition that the function must be analytical? This would make the problem a lot harder. $\endgroup$ – colt_browning Jun 9 at 20:35

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