Q1) The precise definition of lim x->a (f(x)≠L) is as follows

There exists an ε>0 such that for every δ>0 and if 0<|x-a|<δ then |f(x)-L|>ε

Show that lim x->0 sin(pi/x)≠L

note: Take L=0.19

Q2) Calculate lim x->1 (sqrt(x+8)) and prove it by using ε and δ definition of limit.