32 Part I: The Questions
190. lim
x
x
x
→−
+
+
5
1 5
1
5
191. lim x x
x x
→
+
−






0
1
1
1
192. lim
(
)
h
h
h
→
−
−
+
−
0
1
1
4
4
Applying the Squeeze Theorem
193–198 Use the squeeze theorem to evaluate
the given limit.
193. If 5 ≤ f
 
(x) ≤ x
2
+ 3x – 5 for all x, find lim ( )
x
f x
→2
.
194. If x
2
+ 4 ≤ f
 
(x) ≤ 4 + sin x for –2 ≤ x ≤ 5,
find lim ( )
x
f x
→0
.
195. If 2x ≤ f
 
(x) ≤ x
3
+ 1 for 0 ≤ x ≤ 2,
evaluate lim ( )
x
f x
→1
.
196. Find the limit: lim cos
x
x
x
→






0
4
2
2 .
181. lim x
x
x
→
−
−
3
4
81
3
182. lim
x
x
x
→
+
+


 


 
0
2
2
2
183. lim
x
x
x
→
−
−


 


 
0
2
2
2
184. lim
x
x
x
x
→
−
−
4
3
2
3
4
3
4
185. lim x
x
x
x
→
−
−
+
5
2
2
25
3
16
5
186. lim x
x
x
x
x
→
+ −
−
3
2
3
2
3
187. lim
(
)
h
h
h
→
+
−
0
3
2
8
188. lim
x
x
x
→
+
−
−
4
4
4
189. lim
x
x
x
→
−
−
−
5
5
5