Deﬁnition :. We say that a function f is continuous at a provided that for any ε > 0, there exists a δ > 0 such that if |x−a| < δ then |f(x)−f(a)| < ε.
(a) Use the deﬁnition of continuity to prove that lnx is continuous at 1. [Hint: You may want to use the fact |lnx| < ε ⇔−ε < lnx < ε to ﬁnd a δ.]
(b) Use part (a) to prove that lnx is continuous at any positive real number a. [Hint: ln(x) = ln(x/a) + ln(a). This is a combination of functions which are continuous at a. Be sure to explain how you know that ln(x/a) is continuous at a.]
for part a how can I find δ that works for if |x−a| < δ then |f(x)−f(a)| < ε. and for part b how can I show that ln(x/a) is continuous at a ?
please help me with part a and b