Module 6 - Continuity

Module 6 - Answers

Lesson 1

Answer 1

6.1.1 Evaluate

and f(0).

It may be faster to copy and paste the previous commands from the History Window to the Edit Line and change to 0.

Although exists, f(0) is undefined. Therefore, is not continuous at x = 0.

Lesson 2

Answer 1

6.2.1 From the graph, it appears

and

, which suggests an infinite discontinuity.

Lesson 3

Answer 1

6.3.1 The left- and right-hand limits are

and

The function will be continuous if these limits are equal. Setting 2 + k = 5 gives k = 3. So if k = 3, and the function is continuous.

Answer 2

6.3.2 The function will be discontinuous at x = 2. The parabolic piece of the graph will be shifted up so that it does not connect with the linear piece.

Answer 3

6.3.3

Self Test

Answer 1

II and III

Answer 2

A removable discontinuity (hole) can be seen at at x = –1

The window shown is [–7.9, 7.9] x [–3.8, 3.8] (ZoomDec) with xres = 1.

Answer 3

k = 0

Answer 4

The window shown is [–7.9, 7.9] x [–3.8, 3.8] (ZoomDec)

Answer 5