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Byju's Answer
Standard XII
Mathematics
Function Defintion
The value of ...
Question
The value of
lim
t
→
0
⎛
⎜ ⎜
⎝
−
1
t
2
⋅
t
2
∫
2
t
sin
t
d
t
⎞
⎟ ⎟
⎠
equals to
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Solution
Let
L
=
lim
t
→
0
⎛
⎜ ⎜
⎝
−
1
t
2
⋅
t
2
∫
2
t
sin
t
d
t
⎞
⎟ ⎟
⎠
(
0
0
)
form
Applying L'hospital rule, we get
⇒
L
=
lim
t
→
0
sin
t
2
⋅
2
t
−
sin
2
t
⋅
2
−
2
t
⇒
L
=
lim
t
→
0
(
−
sin
t
2
+
2
sin
2
t
2
t
)
⇒
L
=
0
+
2
=
2
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