Textbook pdf's

3. What are the basic types of discontinuity? Give an example of each.
4. Find the value(s) of x at which each function is discontinuous.
13x
a. c. h1x2 x2 1
f 1x2 9 x2
e. g1x2
x 3
x 3
x 2 x 6
x, if x 3
b. g1x2 7x 4 d. f 1x2 x 4 f. h1x2 e
x
x 2 9
1 x, if x 7 3
K
A
PART B
5. Determine all the values of x for which each function is continuous.
a. f 1x2 3x 5 2x 3 x c. h1x2 x2 16
x 2 5x
e. g1x2 10 x
b. g1x2 px 2 4.2x 7 d. f 1x2 Vx 2 f. h1x2 16
x 2 65
6. Examine the continuity of g1x2 x 3 when x 2.
7. Sketch a graph of the following function:
x 1, if x 6 3
h1x2 e
5 x, if x 3
Determine if the function is continuous everywhere.
8. Sketch a graph of the following function:
f 1x2 e x2 , if x 6 0
3, if x 0
Is the function continuous?
9. Recent postal rates for non-standard and oversized letter mail within Canada
are given in the following table. Maximum dimensions for this type of letter
mail are 380 mm by 270 mm by 20 mm.
100 g or Less
Between 100 g
and 200 g
Between 200 g
and 500 g
$1.10 $1.86 $2.55
Draw a graph of the cost, in dollars, to mail a non-standard envelope as a
function of its mass in grams. Where are the discontinuities of this function?
10. Determine whether f 1x2 x2 x 6
is continuous at x 3.
x 3
11. Examine the continuity of the following function:
x, if x 1
f 1x2 • 1, if 1 6 x 2
3, if x 7 2
52
1.6 CONTINUITY
NEL