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AIEEE 2003 Math Solved Paper
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© examsnet.com
Question : 62
Total: 66
Let
f
(
a
)
=
g
(
a
)
=
k
and their
n
th
derivatives
f
n
(
a
)
,
g
n
(
a
)
exist and are not equal for some
n
. Further if
lim
x
→
a
f
(
a
)
g
(
x
)
−
f
(
a
)
−
g
(
a
)
f
(
x
)
+
f
(
a
)
g
(
x
)
−
f
(
x
)
=
4
then the value of
k
is
0
4
2
1
Validate
Solution:
lim
x
→
a
f
(
a
)
g
′
(
x
)
−
g
(
a
)
f
′
(
x
)
g
′
(
x
)
−
f
′
(
x
)
(By
L
′
Hospital rule)
lim
x
→
a
k
g
′
(
x
)
−
k
f
′
(
x
)
g
′
(
x
)
−
f
′
(
x
)
=
4
∴
k
=
4
.
© examsnet.com
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