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Byju's Answer
Standard XII
Mathematics
Expansions to Remove Indeterminate Form
Evaluate the ...
Question
Evaluate the limit:
lim
x
→
0
x
c
o
s
x
+
2
s
i
n
x
x
2
+
t
a
n
x
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Solution
We have,
lim
x
→
0
x
c
o
s
x
+
2
s
i
n
x
x
2
+
t
a
n
x
It becomes 0/0 form.
=
lim
x
→
0
x
(
c
o
s
x
+
2
s
i
n
x
x
)
x
(
x
+
t
a
n
x
x
)
=
lim
x
→
0
(
c
o
s
x
+
2
s
i
n
x
x
)
(
x
+
t
a
n
x
x
)
[
∵
lim
x
→
0
s
i
n
x
x
=
1
,
lim
x
→
0
t
a
n
x
x
=
1
,
lim
x
→
0
c
o
s
x
=
1
]
=
1
+
2
×
1
0
+
1
=
3
Therefore,
lim
x
→
0
x
c
o
s
x
+
2
s
i
n
x
x
2
+
t
a
n
x
=
3
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Standard XII Mathematics
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