Part II: The Answers
202
Then substitute 0 into the equation and solve:
lim
sin
sin
cos
cos
( )
x
x
x
x
x
x
→
+
( )
=
+ ( )
= +
=
0 1
1
1
1 1 1
0
1
1 1 1
1
2
207.
∞
As x approaches 3 from the left, the y values approach ∞ so that lim ( )
x
f x
→
−
= ∞
3
.
208.
–∞
As x approaches 3 from the right, the y values approach –∞ so that lim ( )
x
f x
→
+
= −∞
3
.
209.
∞
As x approaches 5 from the left, the y values approach ∞ so that lim ( )
x
f x
→
−
= ∞
5
.
210.
–∞
As x approaches 5 from the right, the y values approach –∞ so that lim ( )
x
f x
→
+
= −∞
5
.
211.
limit does not exist
As x approaches 5 from the left, the y values approach ∞. However, as x approaches 5
from the right, the y values approach –∞. Because the left-hand limit doesn’t equal the
right-hand limit, the limit doesn’t exist.
212.
∞
As x approaches 1 from the right, you have (x – 1) → 0
+
so that
3
1
3
0
x −
→
→∞
+
Note that the limit is positive infinity because dividing 3 by a small positive number
close to zero gives you a large positive number.
Answers
201–300