Math 220 Worksheet 5
Limits −Section 2.2
1. For the lim
x→af(x) to exist, what must be true?
2. Use the following graph of f(x) to state the value when approaching each quantity. If it does not exist, explain
why.
−5−4−3−2−1 1 2 3 4 5
−4
−3
−2
−1
1
2
3
4
5
6
x
y
(a) lim
x→−2−
f(x)
(b) lim
x→−2+f(x)
(c) lim
x→−2f(x)
(d) f(−2)
(e) lim
x→2−
f(x)
(f) lim
x→2+f(x)
(g) lim
x→2f(x)
(h) f(2)
3. Sketch the graph of the function and use it to determine the values of a for which lim
x→af(x) exists.
f(x) =
exif x≤0
x−1 if 0 <x<1
ln(x) if x≥1
