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Byju's Answer
Standard XIII
Mathematics
L'Hospital Rule to Remove Indeterminate Form
If limx→1x2-a...
Question
If
lim
x
→
1
x
2
−
a
x
+
b
x
−
1
=
5
,
then
a
+
b
is equal to :
A
1
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B
5
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C
−
4
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D
−
7
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Solution
The correct option is
D
−
7
Given
lim
x
→
1
x
2
−
a
x
+
b
x
−
1
=
5
In order to limit exist, numerator must be equal to
0
at
x
=
1
⇒
(
1
)
2
−
a
(
1
)
+
b
=
0
1
−
a
+
b
=
0
a
−
b
=
1
.
.
.
(
1
)
Now, applying L'hospital Rule
lim
x
→
1
2
x
−
a
1
=
5
⇒
2
−
a
=
5
⇒
a
=
−
3
.
.
.
(
2
)
putting the value of
a
in
(
1
)
∴
b
=
−
4
⇒
a
+
b
=
−
7
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0
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