70 STEP 4. Review the Knowledge You Need to Score High
- Givenf(x) as shown in Figure 5.5-2, find
(a) f(3).
(b) xlim→ 3 +f(x).
(c) xlim→ 3 −f(x).
(d) limx→ 3 f(x).
(e) Isf(x) continuous atx=3? Explain
why or why not.
[–2,8] by [–4,7]
Figure 5.5-2- A function fis continuous on [−2, 2] and
some of the values off are shown below:
x − 2 0 2
f(x) 3 b 4If fhas only one root,r, on the closed
interval [−2, 2], andr=/0, then a possible
value ofbis
(A) − 2 (B) − 1 (C) 0 (D) 1- Evaluate limx→ 0
1 −cosx
sin^2 x
.
5.6 Cumulative Review Problems
- Write an equation of the line passing
through the point (2,−4) and
perpendicular to the line 3x− 2 y=6. - The graph of a functionf is shown in
Figure 5.6-1. Which of the following
statements is/are true?
I.xlim→ 4 −f(x)=3.
II.x=4 is not in the domain of f.
III. xlim→ 4 f(x) does not exist. - Evaluate limx→ 0
| 3 x− 4 |
x− 2
.
- Find limx→ 0
tanx
x
.
- Find the horizontal and vertical
asymptotes off(x)=
√x
x^2 + 4
.
8 7 6 5 4 3 2 10123456789yxfFigure 5.6-15.7 Solutions to Practice Problems
Part A The use of a calculator is not
allowed.- Using the product rule,
limx→ 0 (x−5)(cosx)=
[
limx→ 0 (x−5)][
limx→ 0 (cosx)]=(0−5)(cos 0)=(−5)(1)=−5.
(Note that cos 0=1.)