Hi, I have real analysis questions.

I need your help.

Thanks a lot.

3) Let f(x) = sin(1/x) for x E (0, oo). Define f(0) to be any real number of your choosing. Argue that Jon f exists, and it is independant of your choice for f (0).6) Where is the function f differentiable? And compute the derivative where it exists. f (2 ) = x sin x = 0 Where is the derivative continuous? Hint: Other than the theorems from the lecture notes, you will need to know standard facts about the trig functions sin and cos, for example, that sin' = cos, that these functions are continuous, bounded and periodic. Feel free to use any standard facts about sin and cos, such as what you can find on the Wikipedia page