Page 50 - Calculus Workbook For Dummies
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34 Part II: Limits and Continuity
Taking a Closer Look: Limit
and Continuity Graphs
In this section, you get more practice at solving limit and continuity problems visually.
Then in Chapter 4, you solve limit problems numerically (with your calculator) and
symbolically (with algebra).
Use Figure 3-2 to answer problems 5 through 10.
y
20
15
10
f (x)
5
Figure 3-2:
1
Another x
bizarre -10 -5 -1 1 5 10 15 20
graph.
Q. lim f x = ? Q. lim f x = ?
^ h
^ h
x " 0 x " 13
A. lim f x = 2 Because f 0 = 2 and because A. lim f x = 2 because there’s a hole at
^ h
^ h
^ h
x " 0 x " 13
f is continuous there, the limit must equal _ 13 , 2i. The limit at a hole is the height
the function value. Whenever a function of the hole.
passes through a point and there’s no dis-
continuity at the point, the limit equals the
function value.
