- #1
JonF
- 621
- 1
I’m having trouble showing that Sin(x) is a continuous function. I’m try to show it’s continuous by showing: [itex] 0<|x - x_0| < d => |sin(x) - sin(x_0)|<\epsilon[/itex]
Here is what I have done [itex] |sin(x)| - |sin(x_0)|<|sin(x) - sin(x_0)|<\epsilon [/itex] and |sin(x)|<|x| so -|x| < -|sin(x)| => [itex] |sin(x)|- |x| < |sin(x)| - |sin(x_0)|< \epsilon [/itex] but I can’t seem to go anywhere from there.
Here is what I have done [itex] |sin(x)| - |sin(x_0)|<|sin(x) - sin(x_0)|<\epsilon [/itex] and |sin(x)|<|x| so -|x| < -|sin(x)| => [itex] |sin(x)|- |x| < |sin(x)| - |sin(x_0)|< \epsilon [/itex] but I can’t seem to go anywhere from there.