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JEE Main Math Class 12 Limits and Derivatives Part 2 Questions
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© examsnet.com
Question : 39
Total: 56
If
lim
x
→
0
e
a
x
−
cos
(
b
x
)
−
c
x
e
−
c
x
2
1
−
cos
(
2
x
)
=
17
, then
5
a
2
+
b
2
is equal to
[13-Apr-2023 shift 2]
76
72
64
68
Validate
Solution:
lim
x
→
0
e
a
x
−
cos
b
x
−
c
x
e
−
c
x
2
1
−
cos
2
x
=
17
On expansion
lim
x
→
0
(
1
+
a
x
+
(
a
x
)
2
2
!
+
.
.
.
)
−
(
1
−
(
b
x
)
2
2
!
+
.
.
.
)
−
c
x
2
(
1
−
c
x
+
(
c
x
)
2
2
!
)
(
1
−
cos
2
x
(
2
x
)
2
)
×
(
2
x
)
2
=
17
lim
x
→
0
x
(
a
−
c
2
)
+
x
2
(
a
2
2
+
b
2
2
+
c
2
2
)
1
2
(
4
x
2
)
=
17
For limit to be exist
a
−
c
2
=
0
⇒
c
=
2
a
⇒
a
2
2
+
b
2
2
+
c
2
2
2
=
17
⇒
a
2
2
+
b
2
2
+
4
a
2
2
=
34
⇒
5
a
2
+
b
2
=
68
© examsnet.com
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