f is a continuous function defined on D and (i) {xn} converges to x (ii) {xn} is a Cauchy sequence.

Let f be a continuous function defined on D (D is a subset of R) and {xn} is a sequence in D,
(a) Examine if {f(xn)} converges to f(x) if {xn} converges to x (x belongs to D)
(b) Examine if {f(xn)} is a Cauchy sequence if {xn} is a Cauchy sequence.

Continuous functionConvergent sequenceCauchy sequence