Answer the following questions about discontinuities produced by the quotient of two real functions.
a. (i) Define (a) removable (point) discontinuity and (b) infinite (essential) discontinuity at a point.
b. (ii) Construct a rational function that has a removable discontinuity at x=2 and justify your classification using limits.
c. (iii) Construct a rational function that has an infinite discontinuity at x=2 and justify your classification using limits.
d. (iv) Briefly explain, in words, how the behaviour of the denominator in a quotient distinguishes the two kinds of discontinuities you have illustrated above.