33
Chapter 3: Limits and Rates of Change
205. lim
sin(
)
x
x
x
x
→
−
+ −
2
2
2
6
206. lim sin
tan
x
x
x
x
→
+
0
Infinite Limits
207–211 Find the indicated limit using the given
graph.
207.
lim ( )
x
f x
→
−
3
197. Find the limit: lim sin
x
x
x
→
+






0
2
2 .
198. Find the limit: lim
sin
x
x
x
→
+
−
( )






0
3
2
3
π .
Evaluating Trigonometric
Limits
199–206 Evaluate the given trigonometric limit.
Recall that lim sin
x
x
x
→
=
0
1 and that lim cos
x
x
x
→
− =
0
1 0.
199. lim
sin( )
x
x
x
→0
5
200. lim cos
sin
x
x
x
→
−
0
2
2
201. lim cos
sin
cos
x
x
x
x
→
−
π
4
2
202. lim
sin( )
sin( )
x
x
x
→0
5
9
203. lim
tan( )
sin( )
x
x
x
→0
7
3
204. lim
sin ( )
x
x
x
→0
3
3
2