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JEE Main Math Class 12 Limits and Derivatives Part 1 Questions
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© examsnet.com
Question : 6
Total: 100
Let
β
=
lim
x
→
0
α
x
−
(
e
3
x
−
1
)
α
x
(
e
3
x
−
1
)
for some
α
∈
ℝ
. Then the value of
α
+
β
is :
[26-Jul-2022-Shift-2]
14
5
3
2
5
2
7
2
Validate
Solution:
β
=
lim
x
→
0
α
x
−
(
e
3
x
−
1
)
α
x
(
e
3
x
−
1
)
,
α
∈
R
=
lim
x
→
0
α
3
−
(
e
3
x
−
1
3
x
)
α
x
(
e
3
x
−
1
3
x
)
So,
α
=
3
(to make independent form)
β
=
lim
x
→
0
1
−
(
e
3
x
−
1
3
x
)
3
x
=
1
−
(
3
x
+
9
x
2
2
+
.
.
.
.
.
)
3
x
3
x
=
−
(
9
2
x
2
+
(
3
x
)
3
31
+
.
.
.
.
.
)
9
x
2
=
−
1
2
∴
α
+
β
=
3
−
1
2
=
5
2
© examsnet.com
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