hey guys. so im in an introductory real analysis course and I am finding it quite challenging, partially because my teacher isnt great. i went to ask for help on some limit problems but im not sure if his advice was accurate.
1) Find lim(x approaches x0-) f(x) and lim((x approaches x0+) f(x) for f(x)=(x+abs(x))/x x0=0 i found the solutions (2, x>0 and 0, x<0) easily. The book asks for an epsilon-delta proof if possible and my teacher claims it is trivial because they are constant. if this is the case when should you finish the proof?
2) I would also appreciate help with a second problem that asks the same thing except when f(x)= abs(x-1)/(x2 +x-2), x0=1
3) prove: if limf(x) exists, there is a constant M and a p>0 such that abs(f(x)) < or = M if 0<abs(x-x0)<p. I was having trouble with this one also. in this case, basically p is delta right? and if we assume f(x)=M, then abs(M-L)=epsilon. should i approach this proof with a contradiction?
thanks for all advice!