Assume that (xn) is a sequence of real numbers and that a, b € R with a is not eaqual to 0.
(a) If (x_{n}) converges to x, show that (|ax_{n} + b|) converges to |ax + b|.(b) Give an instance , with brief justication, where (|x_{n}|) converges but (x_{n}) does not.(c) If (|x_{n}|) converges to 0, elustratethat (xn) converges to 0.
In (a) you need to use only the denition of convergence and no other limit theorems.