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Byju's Answer
Standard XII
Mathematics
Definition of Functions
Find the li...
Question
Find the
lim
x
→
0
(
x
+
4
)
3
/
2
+
e
x
−
9
x
without using L'Hospital rule
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Solution
(
x
+
4
)
3
/
2
=
8
(
1
+
x
4
)
3
/
2
(
1
+
x
/
m
)
n
=
1
+
n
x
m
+
n
(
n
−
1
)
2
!
x
2
m
2
+
.
.
.
.
.
Hence expansion of
(
1
+
x
4
)
3
/
2
=
1
+
3
2
x
+
(
3
2
)
(
1
2
)
2
!
x
2
.
.
.
.
.
now expansion of
e
x
=
1
+
x
1
!
+
x
2
2
!
+
.
.
.
.
.
now put these expansion on given expression
lim
x
→
0
(
x
+
4
)
3
/
2
+
e
x
−
9
x
=
8
(
1
+
3
2
x
4
+
3
8
x
2
4
2
)
+
(
1
+
x
1
!
+
x
2
2
!
)
−
9
x
On solving this equation we will get
lim
x
→
0
(
x
+
4
)
3
/
2
+
e
x
−
9
x
=
4
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0
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