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Byju's Answer
Standard XII
Mathematics
Rationalization Method to Remove Indeterminate Form
Evaluate the ...
Question
Evaluate the following limits
lim
x
→
3
x
2
−
9
x
2
(
x
2
−
6
x
+
9
)
Open in App
Solution
lim
x
→
3
(
x
2
−
9
)
x
2
(
x
2
−
6
x
+
9
)
⇒
lim
x
→
3
(
x
2
−
9
)
x
4
−
6
x
3
+
9
x
2
this is of the form
0
0
∴
we can differentiate by using L'hospital rule
⇒
lim
x
→
3
[
d
d
x
(
x
2
−
9
)
d
d
x
(
x
4
−
6
x
3
+
9
x
2
)
]
⇒
lim
x
→
3
2
x
4
x
3
−
18
x
2
+
18
x
⇒
2
(
3
)
4
(
2
3
)
−
18
(
2
2
)
+
18
(
2
)
⇒
6
32
−
18
(
4
−
2
)
⇒
6
32
−
36
⇒
−
6
4
⇒
−
3
2
∴
lim
x
→
3
(
x
2
−
9
)
x
2
(
x
2
−
6
x
+
9
)
=
−
3
2
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Standard XII Mathematics
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