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Attempt following question by selecting a choice to answer.
e
Evaluate:
lim
x
→
0
sin
2
7
x

sin
9
x
sin
1
1
x

sin
9
x
+
sin
7
x
e e
A.
e
∞
B.
e
2
C.
e
Does not exist
D.
e
0
E.
e
4
3
e
B
View Solution Steps
Step 1:
lim
x
→
0
sin
2
7
x

sin
9
x
sin
1
1
x

sin
9
x
+
sin
7
x
[The limit is of the form
0
0
.]
Step 2: =
lim
x
→
0
2
7
cos
2
7
x

9
cos
9
x
1
1
cos
1
1
x

9
cos
9
x
+
7
cos
7
x
[Use L'Hôpital's Rule .]
Step 3: =
2
7

9
1
1

9
+
7
[Evaluate the limit.]
Step 4: =
18
9
= 2[Simplify.]
Step 5:
lim
x
→
0
sin
2
7
x

sin
9
x
sin
1
1
x

sin
9
x
+
sin
7
x
= 2
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