# Can anyone guide me for this question?

1. Sep 20, 2014

### Unusualskill

Let f be the function:
f(x) =
sin(x) ; x is element of Q
cos(x) ; x is not element of Q
Prove, using epsilon-delta definition, that there is a point c,which is element of R at which f is continuous.
Hint: Consider c such that sin(c) = cos(c); why does such a c exist? Then,
since you know that sin(x) and cos(x) are continuous at c, for epsilon> 0, you get delta1 >
0 that gives lsin(x)-sin(c)l <epsilon , and also delta2 > 0 that gives lcos(x)-cos(c)l <epsilon .
Now, why does delta = min(delta1; delta2) work to show lf(x)- f(c)l < epsilon.

2. Sep 20, 2014

### HallsofIvy

Staff Emeritus
You were given those "hints", right? So where is your work? Have you found c such that sin(c)= cos(c)?

Why was this posted under "Differential Equations"?