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Standard XII
Mathematics
Substitution Method to Remove Indeterminate Form
Question
lf
lim
x
→
0
(
cos
4
x
+
a
cos
2
x
+
b
x
4
)
is finite then the value of
a
,
b
respectively are
−
5
,
−
4
5
−
4
−
4
,
3
4
,
5
A
−
5
,
−
4
B
5
−
4
C
−
4
,
3
D
4
,
5
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Solution
Verified by Toppr
lim
x
→
0
(
cos
4
x
+
a
cos
2
x
+
b
x
4
)
As
x
→
0
, denominator tends to 0, so the numerator also tends to 0.
⇒
lim
x
→
0
cos
4
x
+
a
cos
2
x
+
b
=
0
at
x
=
0
⇒
cos
4
x
=
1
,
cos
2
x
=
1
⇒
1
+
a
+
b
=
0
⇒
a
+
b
=
−
1
Now, put
a
=
−
4
⇒
b
=
3
Option C satisfies above equation.
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Similar Questions
Q1
lf
lim
x
→
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cos
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+
a
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+
b
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)
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Q2
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)
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Q4
lim
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Q5
Let
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