Answer the following questions related to the basic idea of a limit and continuity.
a. (i) Define the limit of a function f(x) as x approaches a real number a. State the meaning of the notation x→alimf(x)=L.
b. (ii) State the rule that allows you to evaluate x→alimf(x) by simply substituting x=a when f(x) is a polynomial or a rational function whose denominator is non–zero at x=a.
c. (iii) Give two distinct examples of elementary functions that are continuous at every point of their domains and briefly justify your choices.