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