Assignment:
Show that the following limits do not exist: use def. of convergence or cauchy or epsilon delta
a. lim as x goes to 0 of (1/(x^2)) x>0
b. lim as x goes to 0 of (1/(x^1/2)) same as (1/sqrtx)
c. lim as x goes to 0 of (x + sgn(x))
d. lim as x goes to 0 of sin(1/(x^2))
let f: R---> R be defined by setting f(x)= x if x is rational and f(x)=0 if x is irrational.
Show that if L=0 then lim as x goes to c of f(x) is 0
Provide complete and step by step solution for the question and show calculations and use formulas.