MATH 221 Homework on Classifying Discontinuities (Due Wednesday, September 18)

1. . Find and classify the discontinuities of the function defined below. Show all the necessary limits and clearly specify the discontinuities.

a) .

b)

2. Give an example (by formula) of a function, f(x), that has a removable discontinuity at x = 2 and an essential discontinuity at x = 4.

3. For what value of a is the following function continuous at x = 1?