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JEE Main Math Class 12 Limits and Derivatives Part 2 Questions
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© examsnet.com
Question : 14
Total: 56
If
α
=
lim
x
⟶
0
+
(
e
√
tan
x
−
e
√
x
√
tan
x
−
√
x
)
and
β
=
lim
x
⟶
0
(
1
+
s
i
n
x
)
1
2
cot
x
are the roots of the quadratic equation
ax
2
+
bx
−
√
e
=
0
, then 12
log
e
(
a
+
b
)
is equal to _________.
[8 Apr 2024 Shift 2]
Your Answer:
Validate
Solution:
👈: Video Solution
α
=
lim
x
⟶
0
+
e
√
x
(
e
√
tan
x
−
√
x
−
1
)
√
tan
x
−
√
x
=
1
β
=
lim
x
⟶
0
(
1
+
s
i
n
x
)
1
2
cot
x
=
e
1
∕
2
x
2
−
(
1
+
√
e
)
+
√
e
=
0
a
x
2
+
b
x
−
√
e
=
0
On comparing
a
=
−
1
,
b
=
√
e
+
1
12
ln
(
a
+
b
)
=
12
×
1
2
=
6
© examsnet.com
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